A simple solution of something like +1 point of uncertainty (1/3 of a point of sigma) per day would be a good idea imo. https://forum.faforever.com/topic/2767/rating-sigma-should-increase-over-time?_=1652198278795
(Note that 1 point of uncertainty per day is an arbitrary example; the point is that rating sigma would increase by X every Y period)
Also, the league system doesn't solve the problem for global rating, and unless it does something like increasing a player's sigma, I don't see how it really solves the problem for matchmaker ratings either. After not playing in a particular queue for a long time, a player could be a lot better or worse in that game type, and their sigma should be higher to properly match that increased uncertainty. The increased sigma value would allow the player's rating to more quickly adjust and would yield fairer/better matches faster, on average.