bishop exchange early

Gets the castling done quick.

Weakens the pawns in front of the castled king and gives up one of the defenders, ignores development and does nothing to fight for control of the center.

black needs to keep the dark bishop to protect the king after castling

 In the final position after black castles white simply plays h4! intending h5 with queenside castling and an open h file trust me white is doing well here

Bh6?? is an entirely and inexcusably wasteful move. Misplaces Knight, weakens King, loses control of long diagonal.

And why would White give Black a pass by playing 4. e3 ...?

And why would White give Black a pass by playing 4. e3 ...?

As pointed out, there are several flaws with this idea, but I think the important thing is that players try to come up with ideas on their own (rather than memorising an opening manual) and so I commend your efforts.