It releases the tension and black establishes a wedge pawn on e4 and white needs to spend a move repositioning the king's knight after Bxe7. You also mean 6.e3,h6 but we all make those kind of notation slips every now and then. Sometimes I forget to write down captures leading to an awkward scoresheet. Why would black shoo the bishop after castling? Shouldn't it be done before so he doesn't give white an h6 lever to play against with his king there?
Black also can also reinforce the e4 pawn with ...f5 at the proper moment.
1.d4 d5 2.c4 e6 3.Nf3 Nf6 4.Bg5 Be7 5.Nc3 0-0 6.e3 h3 7.Bh4 Ne4 8.Nxe4
What is wrong with white's last move? Doesn't itgive a clear advantage as black's structure is damaged and he has wasted time?