I think extraction shooters will be a big genre too, but not in the way you think it will.
I think PvE extraction shooters are the "next big thing". Just look at the three most successful extraction shooters:
Arc Raiders (which lets face it, most people play it as co-op PvE, not PvP), Helldivers II (another co-op PvE), and Escape from Duckov (a single player PvE). The three extraction shooters with the highest CCU peak are all PvE, and its not even close.
PvP isn't the draw for extraction shooters, PvE and co-op is. Judging from the statistics at least.