But that's part of the point. It largely wouldn't affect them. The current OGL and SRD is enough. An updated SRD would be nice but it wouldn't stop Kobold press at all.
I think it's an open question. There are a lot of new, casual players for whom D&D is what's on DNDBeyond. Granted, that's not Kobold Press's audience anyway. But a move like this would lessen the chances of a Kobold Press ever reaching some of that crowd.
I do think this would be a self-lacerating move on WotC's part, but that doesn't mean they won't do it. From the mindset of a conventional corporate manager, the OGL and SRD are aberrations. It depends how well the people calling the shots on this one understand the history and culture of the game, and what a big role open sourcing 5E played in D&D's success since 2014.