The 'quick training' theory has been mentioned on CHF for ease of use of the dao over the jian, and perhaps it may contribute a little to the prominence of the dao in the Han period and after. It is not the primary reason IMO.
I have thought rather a lot about the Han dao design, and there is another reason (as given by Cheng & Dong in 'Ancient Chinese Weapons') and this is the increasing prominence of cavalry in the Han period. Chariots disapear, and with the the hooking ge halberd. The % of cavalry in Han armies is much greater than the % in the Qin buried army for example.
The use of a dao, the straight edged sabre, is suited to horseback and slashing in an arc. Han art depicts these swords being carried by horsemen on a number of occasions.
There is also the infantry dao shown in art, and a range of sizes, which means Cheng & Dong simplify the reasons too much just like a 'training' hypothesis.
My main feeling is that the quality of steel in the Han, the improvements contemporaneous with this change to the dao, contribute a lot. Yang Hong also in his book 'Ancient Chinese weapons' considers the dao the primary weapon of the period rather than the jian.
I should however correct the thread title. The jian was never 'abandoned'. It was always used, and the form persists long after the ring pommeled type of dao vanishes. Both short jian and more still the long jian can still be found in the Han period in quite some numbers.
Jeroen of swordforum mentioned recently, and he has first hand knowledge, that the length of iron swords is because making/forging a long iron sword is not much harder than making a short one. With casting bronze the difficulty is increased with length due to the requirments of temperature and metal flow through the mold. There are other reasons too that bronze is not quite as practical for long weapons. The weight 1 ti 1 with iron and the chance of flaws along the length.
To return to the topic, when steel appears and in the Han is refined the longer blades become the main type.
With a long jian of 1m or more wielding it to thrust is much more difficult, a long sword is better suited for slashing. A short sword is quick to thrust but something more than twice as heavy and balanced further from the hilt means slashing is superior for the 120cm sword.
When swords were of great length they would mostly be used to slash, and here is why a dao is better suited.
The cross section of Han dao focuses ALL onto a blade edge strength. It is weak in a thrust.
There is no crossgaurd so stabbing risks the hand slipping up the blade. The ring pommel allows a lanyard for the wrist and also prevents the sword slipping out the hand from its mass while striking.
A 1m+ jian if used to slash is perhaps more versatile but is not adapted 100% to slash in the same way. The blade is not as strong for the mass due to the cross section.
The Han dao is well suited to its task, given the length of swords being produced the factors of specialisation & cavalry & training all would mean together the long dao would find prominence over the long jian at this time.
PS; here is a bronze Han ring pommeled dao of 70cm. Probably 2nd century BC and much longer than most bronze swords. I will be adding more pictures and updating my Han dao thread later. Steel dao are longer but seldom preserve so well. At this time (early West Han) bronze is made long to compete with the larger steel swords. Once steel was fully mastered by Han Chinese bronze is dispensed with.
The cross section, unique to such dao, can be seen on the Han dao thread;
http://www.chinahistoryforum.com/index.php?showtopic=7440 The fragment from that is shown here for comparison also.
Compare to an
I beam in a steel building support, the outer surface area for mass is greater and so it makes a stronger blade for a slash.

BTW, the sabre above looks much the same as the sabre in the British museum on the link I gave.
The pommel has silk thread mineralised on it from contact in the tomb {seen here just barely as a pattern...when examined at 70x the silk strands can be seen in a weave}, this was the only bare bronze on the sword when buried to preserve the covering.
Fabric on the handle is {not shown} visible at 70x magnification at tiny points & wood grain alignment can be seen imprinted in silt on the blade from a scabbard that decayed long ago.