I think the title of the post is a bit outlandish, it's not for nothing that the Ruy Lopez was played by Ian Nepomniatchi in 4 games in his World Championship match against Magnus Carlsen, none of which Nepo lost, despite losing 4 games in the World Championship match as a whole. Bb5 pressures the pawn on e5 indirectly, threatening Nxc6 Nxb5 (although there are reasons this can't be done immediately).
Is the Ruy Lopez A lie?

Bb5 has some venom in it. It develops your bishop, but it also influences how the opponent can play. For instance, they cannot play d3 or d4 before kicking the bishop because they put themselves in an absolute pin. At this point, enough white pieces may be out to take advantage of this pin, although this is playable with accuracy. Bb5 also requires black to loosen their queenside, and the c pawn can get left behind. This does help create space and a queenside attack, but it also creates weaknesses that can be exploited. Lastly, the bishop eventually lands pointing to the f7 square anyways.
As for castling on move 5, the pawn is very easy to get back. If black tries to hang on to it they can land in tough positions. If black plays poorly, it can even win white a whole piece(s).
A6 does not need to be played. This leads to Berlin endgame, and it's very popular. However, A6 and B5 must be played at some point to counter act the problems posed by the Bishop on b5. If you don't kicking it, you have trouble holding the center because of the pin, and white may even decide to take if it strikes them.
Bishop e7 is the closed lopez. This move seems obvious. The king wants to castle, so the bishop gets out of its way and controls some key squares. The board is going to be very closed and cramped. Black doesn't want the bishop in the way of queenside pawn march, and it also keeps some scope on the kingside where white will launch an attack as they often swing their b knight over.
This is just the stuff I can exploit at my lowly elo. Imagine what a GM sees in such a complex position.
The purpose of move a6 is the same as h6 in Moscow defense (1.d4 d5 2.c4 c6 3.Nc3 Nf6 4.Nf3 e6 5.Bg5 h6 , and now if White plays 6.Bh4, Black can go 6...dxc4 7.e4 g5 8.Bg3 b5, winning a pawn). If White decides to play Bxc6, Black has indeed lost a move - but a good player would not play Bxc6 right away if not unprompted.
If While goes Ba4 and later threatens to capture on c6+e5, Black always gets the option b5. Why Black holds off b5 is on a different topic - but if a6 Ba4 way not played, Black could not get the option to kick off the bishop.