A mass migration to itch.io seems unlikely, given DM’s Guild. I’m also not super familiar with OGL/the SRD but we don’t really want to have to deal with legal issues related to putting D&D content on itch.io either.
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I don't really want to keep this going at this point, but just for future reference, OGL (and most D&D licenses) and the Fate license don't make any explicit restrictions on storefronts. There's no legal issues there - I only want to make that clear so designers stumbling on this aren't scared away from the platform. As long as you follow the license you can host/sell it anywhere.
The WotC FAQ on the OGL (little alphabet soup there), which includes a link to the license itself.
Functionally, two cases:
1. If you directly host open game content (that is, people write whole games on the forum itself, or post big excerpts of mechanics and such), and if that counts as publishing, then the writers of same theoretically need to attach the OGL... Somehow? Nobody does this outside of SRD sites where they host a crapload of it, and nobody apparently cares, though some people do (rarely) link to it.
2. If you host self-contained publications that include open game content (that is, people put OGL systems and stuff up on Itch), then the writers of same need DO need to include the license in the publication. Everybody does this, and indications are that WotC does care, though not to any draconian extent.