"After 4. BxN black now has the bishops pair, which is generally considered at least fair compensation for doubled pawns in most positions,"
Fischer debunks that. With his "Ruy Lopez - Exchange Variation" as White.
https://www.chessgames.com/perl/ezsearch.pl?search=Bobby+Fischer+Ruy+lopez+exchange+variation+
3 Bd5 technically does not waste a tempo.
For less development after 4 BxN it's worth it for it leaves Black with doubled pawns, and an inferior position.
1) Sure it wastes a tempo. You've arrived a position with black to play you could have arrived at with white to play
2) After 4. BxN black now has the bishops pair, which is generally considered at least fair compensation for doubled pawns in most positions, and either 4...dxc3 opens a diagonal for white's bishop (development) or 4...bxc3 gives white added control over the center and an open b-file.