I disagree with using ‘generic fonts’. That’s not how typography works.
You don’t need a Typekit subscription to use better quality fonts from their library. They have a free option as well (limited options). Not all of them are great but they have a better choice than what you would get with Google’s webfonts.
From what I’ve seen, most theme designers use Google fonts. We all know they lack in quality but there are a few that render quite well. Steve Matteson is a well established Type Designer with impressive fonts under his portfolio (Droid Sans/Serif, Open Sans, Noto Sans, Segoe, etc). But that doesn’t give you much diversity.
Have you ever thought of talking to foundries or just the Type Designers themselves about working out a deal?
You could always use typefaces that work best with your theme from whatever webfont distributor you choose. Then, just attach a disclaimer that you’re using (hopefully) quality webfonts from
INSERT DISTRIBUTOR NAME HERE which have been paid for. However, these should not be available in the download unless you have permission.