No, you're not. GS3 was the perfect ending for the serie, it was meant to wrap everything together.
So why Capcom did GS4? Money.
They could have made a totally unrelated game to the precedent serie (a game with you being prosecutor would have been awesome) and it wouldn't have destroyed the continuity.
They didn't. Ok.
And the protagonist is a new character, with his new (shitty) character design...
So what the fuck was in their minds? It's a mistery.