Exchange in the Scotch Four Knights In the main line of the Scotch Four Knights

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1.e4 e5 2.Nf3 Nc6 3.d4 exd4 4.Nxd4 Nf6 5.Nc3 Bb4 6.Nxc6 bxc6 7.Bd3


What's wrong with 7...Bxc3 ?

It seems this move is played very rarely, but, when I play White, I would not like to face it, because of the horrible pawn structure White gets, with isolated doubled pawns and another isolated pawn. For example, see the position after the normal moves 7...Bxc3 8.bxc3 d5 9.exd5 cxd5.  

Of course I see that White gets the Bishops pair and an open b-file, and he can also play Ba3 preventing Black from castling. But is this enough to compensate for the bad pawns? Or is there something else that I don't see? What should be the plan for White after 7...Bxc3 ?
I think you got it basically right. White gets the bishop pair which in an open position like this, is a real advantage. Also black currently does not have any good squares for his pieces. Lastly, it is difficult for black to take advantage or to attack the doubled isolated pawn.

White's dark squared bishop could go to g5 where the pin of the knight is kind of annoying or to a3 where it might hinder black from castling.

Regarding your proposed continuation, I believe that after 7...Bxc3 8.bxc3 d5, white can play 9. e5 asking the knight where it wants to go. Also after black's d5 the a3-f8 diagonal gets weak and the bishop on a3 will be really strong.