If People Can Fly (Painkiller, Bulletstorm) or Croteam (Serious Sam) wanted to take up the challenge, I might be tempted to give it a look. Those two studios really took up the reins for the run-and-gun FPS in the absence of Duke Nukem and his like, anyway.
But after the Colonial Marines fiasco, it's hard not to feel the people who think a second developer would end up playing scapegoat have a point.
As far as the "cultural tone" thing goes, I think one could make a good Duke Nukem game that still played up the 80s-style action hero machismo. Or satirize it, or even be smart enough to do both at the same time, seemingly different things to different people. But first, the character has to be a hero- likable, brave, witty, but above all, competent. Duke of DN3D kind of was that guy, because "his" input was limited to the occasional one-liner in between long stretches of empowering game-play that made the player feel like they were in the boots of a bad-ass. Duke of DNF was the one-eyed man in the village of the blind, or more accurately, the half-wit in the village of idiots. Just about every other character in the game was a blowhard, a bimbo, or an shrieking imbecile. Frequently more than one of the three. And with Duke running for cover every couple of hits and leaving multiple levels flat on his back passing out, it was hard not to think that the hero of any other FPS would be wiping the floor with the opposition and cutting back to piledrive our erstwhile hero without raising a sweat.
Don't tell me how awesome Duke is. Don't have everyone adoring Duke because the narrative insists he's awesome. Show me a Duke who warrants that adoration, and I might even think he's earned the downtime when he's hitting on strippers.