I think you guys are heavily underestimating the changeover of personnel when you talk about a unit having "institutional" experience separate to that of the officer and enlisted who comprise it (and who are killed, wounded or transferred in large numbers). Experience should be built up by combat (and/or whatever mission the unit is supposed to carry out) but eroded by casualties. One of the most obvious examples of how hugely a unit can change over the course of the war to my mind is from WW1. The 16th (Irish) and 10th (Irish) Divisions were as the name suggests, primarily recruited in Ireland at the start of the war. Both saw significant combat on the Western Front and at Gallipoli and in the Middle East. By the end of the war, the 16th had only a single "Irish" battalion remaining, the remainder being English, Scottish and Welsh. The 10th Division ended the war primarily manned by battalions of the Indian Army. Assigning either division any characteristic derived from the exploits of either division earlier in the war wouldn't be sustainable - the men who carried out those exploits were dead, missing, wounded or redeployed elsewhere.
Towards the end of WW2, on the German side in particular, units were thrown together from whatever units and leaders could be found. Giving them an impressive sounding title, or assigning them to a prestigious unit didn't suddenly make old men and young boys become super soldiers. Soldiers and NCOs were dying far too often to absorb, let alone share, unit lessons across a division. The sort of "lessons learned" recap, where a unit integrates experience gained into its training across an entire division or brigade is not done at the side of a road in occupied territory. It happens at the end of wars, or when the unit is taken out of the line for months or years at a time. This sort of time out simply wasn't available on the Soviet, German and after 1942 British/US sides.