Sicilian with 2. Bc4

Your variation (which I play as well) is obviously slightly better for black already, but I find it annoying that white can pressure your d-pawn with moves like Nc3 and Bg5, forcing you to either protect it with your bishop/rook (passive) or move it to d4 when white's bishop on b3/a2 suddenly becomes powerful. Perhaps one should just continue like a normal Sicilian with e6/Nc6/a6 when white will play a4, weakening b4 and forgoing queenside castling, but then white might play like in a Fischer-Sozin (moving a pawn to f5 to undermine e6) where the bishop is useful on c4. I don't think 2.Bc4 is utterly bad for white, even though when beginners play it I want to punish it immediately :P
I get this move quite often against me in blitz.
What is the goal of this move? Most of the times I play against this move the bishop gets to be inert for like 20 moves because it is stuck behind pawns.
is this a correct way?Most of the times I play it like this: