Also, all three of those moves (7. a3, 7. a4 and 7. 0-0) rule out the Velimirovic Attack, which involves castling Q-side.

Doesn't Bb3 fall victim to a Nbd7 line that is arguably better for black? For example, in Logozar's 1.e4 course, he gives this line, where white is down a pawn and needs to prove a draw.

This one, #4, where you commented that white needs to prove a draw. I just meant that I thought it's a clear draw.

Also, all three of those moves (7. a3, 7. a4 and 7. 0-0) rule out the Velimirovic Attack, which involves castling Q-side.

Doesn't Bb3 fall victim to a Nbd7 line that is arguably better for black? For example, in Logozar's 1.e4 course, he gives this line, where white is down a pawn and needs to prove a draw.

This one, #4, where you commented that white needs to prove a draw. I just meant that I thought it's a clear draw.