I'm confused because I've bought players from leagues that aren't enabled plenty of times, but it seems intuitively like more active teams = more players = more regens. Am I wrong?
Adding more nations as playable or view-only will increase the player count and also the number of regens generated. Adding additional leagues within these nations will usually increase the player count, so your intuition is correct.
This post may be helpful if looking for more information on the subject.