The backtracking in 4 was horrible, sure, but Bloody Palace was glorious. Just imagine having Nero, Dante and Vergil playable on Bloody Palace. SO GOOD.
I think the way NT is handling it is spot-on, the main campaign with just one character being their focus with the story they want to tell, and spin-off side-stories for the other characters. I'd even take a Nero DLC for DmC instead of a whole new game, if not for the improvements I really want to see being made that they could only achieve with a sequel.
DMC4 has such great gameplay that they could've kept the game alive up until now with DLC campaigns being released every year, with Nero, Dante and Vergil being playable. Maybe even Trish. It would further expand the lore and give us new things to play with the fantastic combat system. There's nothing fundamentally broken there that desperately needs a sequel.
I hope Capcom can learn a thing or two about creative use of DLC with Ninja Theory. Not gonna lie, I'm a sucker for costumes DLC and things like that, but I'd LOVE new campaigns and gameplay content in general.
Just imagine how CRAZY combo videos would be today if they made a DLC with Dante where you gain access to new weapons and styles and is able to predefine them before you play. It might break the original campaign, but all they have to do is limit its use there. Hell, for all I care DMC4 is pretty much DMC: Bloody Palace Edition anyway.