I don't think you're going to see too many big PSA set collectors crossover to SGC. See this horror story:
Linky
I'm not taking a side in the above thread. The point is if you have a lot of cards invested in PSA at certain grades, you don't want to crossover to SGC at lower grades. And you don't want your set to be half SGC / half PSA, with those cards staying in PSA that don't make the minimum grade. And if SGC guarantees that PSA cards will crossover to SGC at the same grade or better (minus obvious misgrades) kinda like how PSA does their half point reviews, you will melting point anger the SGC core constituency, who will believe SGC is now letting in a bunch of overgraded cards into their pops.
The fact is both PSA and SGC have core fans who strongly follow that TPG for one reason or the other. For myself, more of my collection is in PSA these days, but I still submit to SGC regularly (probably once every couple months or so). I don't think either TPG is going away or falling into GAI-like circumstances. Just choose whichever TPG you want or both.