About later era horse units w/melee-type weapons that don't advance into combat;
The only one I can recall w/certainty is the English Light Brigade. With less certainty, I think the Polish Uhlan and Arabic Camel riders also do this.
Due to the large number of games played, and the consistent way that they've been set up, my own impression is that the units that do this are late game horse units that have melee-type weapons, that are "parallel" to most other horse units using guns. Late Renaissance/early industrial periods, when most horse units are shooting, there are still a few that are using swords and lances. These few seem to be the units not advancing into combat. My impression is that a "category" of late horse units is set up to stand in place and shoot their guns. The units that don't advance, despite using melee-type weapons, are possibly within this "category," which would explain why they don't advance.
Hope this helps.