Any studio could make a Fallout game and nearly all of them would do it better than Bethesda. There's no proprietary knowledge required to do it justice besides genuine love for the series and an understanding of its ideas. The reason we won't see another Obsidian Fallout is because Zenimax isn't going to work with a competitor (Microsoft).
Shit, some random autist on this forum could make a better Fallout game. Shit, lemme do it right now.
Set the next game in Hawaii. No super mutants, no mole rats, almost none of the regular Fallout enemies besides ghouls, feral animals and maybe giant mutated insects... oh, and Deathclaws because the lore states that Deathclaws were created by the US Military from the genetics of Jackson's Chameleons, which are endemic to Hawaii. In fact, fuck the regular Deathclaws, make NEW breeds of Deathclaws. Namely, a breed that retains it's chameleon abilities. Have fun hunting that in the jungles!
Basic intro could be that after that war with the Legion, the victorious NCR continued it's expansion, setting it's eyes across the irradiated oceans to an island only read about in prewar books. For the most part it seems to be an uninteresting place.... except that it was the largest reserve of military power in the US. To that end the NCR has assembled an expedition of interested parties. Caravan companies looking for loot to sell, NCR prospectors looking for new territory to stake out, the NCR military looking to reclaim prewar battleships, even the Brotherhood of Steel sends representatives hoping to get their hands of military tech before the others.
Do something Bethesda seems unable to wrap their tiny little brains around: VEHICLES! Make boats a vital part of traveling between Hawaiian island. Hell, make them damn near essential to fighting the mutated horrors that would be infesting the oceans.
And for fuck's sake don't take it too seriously like Bethesda seems to want to do now. Remember the humor the original games under Black Isles had? DO THAT! How about the only surviving BoS member looses his goddamn mind and tries to refound the BoS with a local tribe, only to end up with a buttload of savages worshipping him as a god and cosplaying as BoS members in coconut power armor costumes? How about there's actually fucking Godzilla in the game as an autokill enemy if you sail too far away from the island? Have fun with it, be cheesy and campy and over the top.