Scotch Game: Why do we play Bc4?

I'm wondering what's the reason for playing Bc4 in the Classic Variation if we're going to put it back on e2 soon after when the knight attacks it?

Is it to protect the d5 square? But after we retreat d5 is again possible and we improved the position of black's knight with tempo.

After 6....Nge7 Black threatens to play d5, so 7 Bc4 prevents that. With the Knight on e5, White can gain a tempo with f4 in many lines. The White Queen and Bishop control g4 so the Knight on e5 is not as strong as it looks. After 8 Be2, 8...d5 is not particularly good after 9 0-0.

Thank you! That clears things up a lot.

I'm trying to learn the Scotch for white and I actually never reached this position so far on move 8, black makes different moves, for example this:

And after black's (slow?) move d6 we can put our bishop on a better diagonal I think, if knight goes to e5 we can retreat to c2. Is that a good plan? I think Nge7 with a plan of d5 no longer works because of this:

And now black can't make the Bxe3 with a threat of checkmate on f2 forcing us to take so the Nb5 move works, right?

After 6...d6, I'd personally go for a quick 7 Qd2 and 8 Nb5, as an improvement on the Blackburne Attack I used to play. The Blackburne Attack objectively isn't that good, but can sometimes work wonders as a surprise weapon, as it can become tricky for Black to deal with the ensuing problems on the board. In the normal Blackburne, however, Black plays d5 in one go, while in your variation d6 has already been played.

The white bishop feels slightly misplaced on d3 to me. Also from a practical/psychological point of view, it’s super unlikely that a player who has committed to a ‘solid’ d6 is then going to suddenly play d5 very soon afterwards without the situation changing much. 

It doesn’t seem like a move that needs specific prep, at worst you should just get a slightly better version of normal lines for white. 

I want the white bishop on c2 in the future so he can control the b1-h7 diagonal. It seems like a more important one to me in the Scotch as the black queen wants to go to g6 in main lines of the scotch and put pressure on the white king. White bishop will prevent that idea.

I've always had troubles with the bishop in this opening, it looks nice on c4 but in practice it's not doing anything. And on e2 it's a bit too passive I think. That's why I want to find a better solution if the opponent lets me by playing the slower d6 or some other move.