Definitely he should do this!

He does need to improve in his writing though...
But this time, he should just continue from DMC1. Vol. 1 of the novel has served as the proper prequel to it already for him... Forget the plot in the DMC Manga (pre-DMC3), DMC3, DMC Anime, DMC4, and DMC4 Deadly Fortune Novels! I have to agree with you there, Hassan! Kamiya didn't even mention the Rebellion or Yamato in his original draft... So that leaves Force Edge/Sword of Sparda or the Alastor as the primary Devil Arm for Dante, with Ifrit secondary.
And I think he should improve DMC2 by adding different melee weapons AKA Devil Arms for Dante and Lucia, not just a redesign of their default weapons. I didn't like the fact you have to move the L Analog to make a different combo; I prefer the Pause Combos like in the rest of the games. This one didn't have that, sadly... Also, a better story, like extending more of Lucia's true origins and how Matier found her in the first place. Also, Dante in DMC2 should have DMC1 Dante's personality.
After DMC2, he should let the story continue to the generations after Dante, meaning the 'improved DMC2' would be Dante's final part of his story. Kamiya-san intended DMC to be a more action-packed, over-the-top, stylish, and less somber version of Castlevania since he is a big fan of that franchise, which is no wonder why DMC1 took place most of the time in a castle. He wanted the Sparda bloodline to be similar to the Belmont Clan; so that means the Sword of Sparda would've fitted a major role similar to the iconic weapon of the Belmont Clan - the Vampire Killer whip. I actually found this out with a fellow user here (DMCGamer1989) prior to my temporary leave here. If anyone here is curious on what I mean, you should all see
my thread of what DMC would have been if it was still under Hideki Kamiya's direction.
Just to let ya'll know why I, along with others here, want Kamiya-san to pick DMC up after DMC1. DMC1 Dante is still and will always be my most favorite incarnation of Dante than those that came after him! Never forget that! 
Edit:
How about letting him improve?
After all, he's the one that started this mess. And he should go clean that mess up.
AM I RIGHT, GUYS?