Colbert and Corden are finally beginning to sprinkle in episodes from 2021 soon. Not sure about the others.
The first problem is that at a certain point if you go too far back you get to the pandemic shows, and much as those are a fascinating time capsule, I can see wanting to distance yourself from those.
Past that, for Colbert specifically, a LOT of his content and humor is political and specifically so, and I can see them not wanting to dip back into first run episodes from the 2016 election up through the pandemic. (And before that, the first year is widely considered to be the worst of the show's run).
For all of the shows but especially Corden and Fallon, a LOT of their episodes also rely on licensed material, music, etc. which would likely be an expensive pain in the ass to re-license. (and especially for Corden, the show's eventually dead regardless).