To be fair, the "Vergil wanted power to protect people" is purely fan assumption and there's barely anything that really confirms this was his intention. I myself included interpreted that quote of Vergil as more in the lines of "You're too weak, Dante. How do you expect yourself to protect anyone if you can't even protect yourself?", which is just his way of looking down on his brother with disappointment. Vergil simply gave me the impression of being borderline insane and wanting power for the mere sake of it.
But truth is, we'll never find out Vergil's real intentions. The game itself is very vague about him and all suplementary material has done a very poor job at elaborating him. The whole theory of his mother's death playing a huge part on it, while plausible in a way, isn't really explained enough to accept it.