Well, everything has plot holes. You're right when you say that you can't fix all of them, especially when the lore of DMC is so vague. But Devil May Cry was never concerned with plot. The sole purpose of each entry was to replicate an action movie experience. It never tried to be awe inspiring or deep and it laughed at it's own absurdity. It's a series that makes no sense and it relishes in it.
My main problem with DmC was that it almost took itself too seriously, and I was beginning not to have fun with it. Whenever it let loose, it was enjoyable, but whenever it attempted storytelling, it felt a bit pretentious and at times mean spirited. Compare that to Devil May Cry 1, 3, and 4, which is choreographed in such a way to make the player feel a whole range of emotions despite how nonsensically that entry fit into the DMC chronology. I'm not asking for a fix to every plot hole in the series. I'm asking for a fun Devil May Cry game.