Hi mariusj,
What you have stated are the text book examples. However, if you start digging into the classical texts deeper, you will find the situations were not as clean cut as you have read in the usual modern school text books.

I know because I also studied the similar modern Chinese text books in Taiwan as well as my grandnieces are studying the modern Chinese text book in mainland China. These re-edited history text books in modern time don't really tell you in those facts in details. Sometimes, they do, but they usually just touch on it a little. I did not read my grandnieces' history books too closely when I was in Hangzhou, but I still remember that I needed to be able to write down the reasons why the armies of the Song or Ming or Qing dynasties became so weak for my essay questions in my history classes and for my High School Entrance exam and for my mock College Entrance Exams 30+ years ago in Taiwan. I don't know whether they still give essay questions nowadays, but I assume they would still ask such questions. What I am trying to say is that even in the modern Chinese history text books (that is NOT the real and undisputed history sources for Chinese history) in both Taiwan and mainland China, I believe they did mentioned a bit of the problems I am trying to describe in my previous posts.
Btw, Ming dynasty's 卫所 on the surface were professional armies, and the 兵戶 (family of soldiers) were supposed to be professional soldiers, but they were peasants in fact!!! Please read carefully in Ming Shi and other Chinese history texts (the original sources, NOT the edited versions) as well as research papers and books published by credible scholars who had studies and researched on Ming dynasty military organizations, etc. These materials will tell you what were the exact duties of these so-call "professional soldiers".
The first Emperor of Ming dynasty, Zhu Yuanzhang decided it would be a good idea to set up these farmer-soldiers in various places 卫所 so that they could be "professional soldiers" at the war time, but farmers at the peace time. However, it was NOT to be so. Most of the times, these soldiers were used as slave-farmers by their commanding officers, and they and their descendents could NOT become anything other than the soldiers even though they were half-starved towards the later part of the Ming dynasty. They were NOT really trained militarily too much because the commanders would need them to farm the lands of the 卫所 and took most the produces from them for the officers' own use.
In addition, the commanding officers would also report more soldiers in their armies than there really were in order to get more soldiers' salaries and food from the central government. These money and food also went into the commanders' own pockets, and NOT the slave-farmer-soldiers!!! What should be rightfully going to these soldiers, about half or maybe more also went into these commanders or officers' pockets. Oh, the scholar bureacrates and the eunuchs that monitored these armies also got their own share of money.
Towards the middle part of Ming dynasty, the government corruption became so bad that the standard army's weapon production became worse and worse. Many of these so-called "professional soldiers", but actually slave-farmers, had no actual swords or spears that could be called "real" swords or spears!!! However, it did not mean the Chinese weapon producing technologies were worse than Japan or other countries. On the contrary, the Chinese craftsmen at the time were producing weapons that were pretty much the leader of the world (or as one of the leaders of the world -- equal to any Western nations as well as Japan). However, if the government officials would not allow these craftsmen to build good weapons for the armies by giving them minimun good iron or steels or money and expecting them to create the same quantity of weapons -- well, the quality really suffered because of these corruptions!!!
Many of these slave-farmer-soldiers were starved and malnutritioned from long time starvations. They were ill trained in any military skills. When they were going into the battle fields, they were either having NO weapons at all or holding toy weapons that looked good (painted or coated with silver powered paints to make them looking like metal from afar) but really were wood or bamboo sticks!!! With these kind of soldiers, that was why there were documents in Ming dynasty (from the middle of the Ming dynasty on probably) that very few (10 to 15 or at most 50) Japanese Pirates could cause hundreds Ming's so-called "professional" soldiers to turn tail and run into the cities and closed the city gates in broad day light!!! Towards the end of the Ming dynasty, these Ming's "professional" soldiers' defeats became totally laughable when facing the Manchurian soldiers -- Please look at the numbers of soldiers in both armies in some of those famously shameful defeats of Ming soldiers and the actual actions of those Ming soldiers. Please think about whether these Ming's "professional" soldiers behaved like the real, well-trained professional soldiers!?
Regarding the Song dynasty soldiers and other Chinese soldiers in previous dynasties, please consider what happened in Ming dynasty and read carefully and in more details of the original sources of those dynasties about what really happened, and NOT what should be.
In China, what really happened usually is/was NOT what should be. It was that way in ancient China, and it was the same now. It does not really matter whether it is in mainland China or Taiwan or Hong Kong. I don't know about Singapore, so I would not include it.
The questions about having the drafted soldiers (from China's great peasant population) or having the professional soldiers (by hiring or installing of the soldiers' families) were always hotly debated in many of the Chinese dynasties and in many of the Chinese Emperors' courts. It is NOT really settled even today. Mainland China used the methods of professional soldiers, but Taiwan used the methods of drafted soldiers (from general populations). Both methods had its own good points and bad points. Even within one Chinese dynasty, this issue would waver back and forth many times. Sometimes, one emperor and his ministers would decide to go for the drafting methods (from the peasant population). Sometimes, another emperor would say, "No, no, no!!! This method is no good, I want to change it to professional soldiers!!!" I remember, even Han dynasty had changed a few times, as well as Tang dynasty. Song dynasty used the mixed methods. The central government's soldiers and the other soldiers were a bit different. One was drafted, and the other was professional. I forgot which was which. Anyway, Song dynasty's soldiers still had the same problems even with both methods!!!
Qing dynasty soldiers were professional soldiers, and they don't need to do anything, but that made them corrupt and became totally useless even faster than earlier dynasties -- It was noted thus by Kangxi when it was in the later years of Kangxi's reign. Fortunately for Kangxi and Yongzhen and Qianlong, they had a few very good commanders and some of the armies were still good enough under these good commanders. When it got to the later Qing Emperors, most of the Qing armies were just plain waste of government money!!! That was why the Qing Emperors needed to rely on the Mongolian armies. Then, when the Taiping Rebellion started, the Qing Emperors had to rely on the privately organized armies by Han scholars, like Zen Guofan, Zhuo Zongtang, Li Hongzhang, etc. Their armies were really peasant armies, and totally private and NOT government's professional armies at all!!! They were the forerunners of the later Chinese warlord armies in the early Republic era!
The corruptions and methods of corruptions lasted from Ming dynasty all the way to the early Republican's armies, including KMT's armies (many of them were actually warlords' armies that became allies with Chiang Kai-Shek and NOT Chiang's own real and really professional modern armies at all!!! Many people always get confused about this fact!!!) It was NOT that Chiang's own professional army officers did not have corruptions.
My mother was in Chiang's own professional army during WWII. Her army was under the command of Chiang's trusted commander, Chen Cheng 陳誠, in Zhejiang area fighting Japanese. However, this so-called "hero of fighting Japanese" (抗日英雄 -- his own son's words when the son, Chen Lu-an 陳履安, was a Presidential Candidate in Taiwan in 1996) seemed to have a corruption problem according to my mother and her army friends. My mom and her army friends were starving, so they went to Chen Cheng's ancestral home in Qingtian 青田縣 (in Zhejiang province) and ate all of Chen Cheng's live stock and took away all his stored food and farm produces!!! His wife (who had bind feet) came out jumping up and down, cursing and crying and yelling at my mom and her army friends, "My husband is a commander, and he would shoot you all!!!" My mother was about 16 years old, and she stood in front of her and yelled back, "Could your husband fight without soldiers? We are starving to death, and your husband has given us no food nor money. Therefore, we are here to eat his own food!" Therefore, I was

when I was listening to Chen Lu-an's campaign speeches in 1996!!!
Anyway, the only way for a Chinese soldier in the old time to have good knives, good weapons, good armors, good food, and good military trainings had always been DIY (Do-It-Yourself)!!! I believe this situation becomes much better after 1950's or so at both mainland China and Taiwan.