Meaning of "going back" in opening, like 9...Nb8 in Ruy Lopez?

As I am targeting rating 1500, very recently I started some learning about openings. I saw a Ruy Lopez line, which seems to be called "Breyer Variation", that surprised me:

The black's move 9...Nb8, in my first impression, was "it's just retreating the knight to the original b8 square". I read that the intention is to do move like 10...Nd7 which is a more active square. However, the knight is moving b8 -> c6 -> b8, finally moving nothing and just wasting 2 out of 9 moves. Even considering 10...Nd7, the knight is spending precious 3 moves just to move from b8 to d7.

It's weird that similar thing happens in other openings, like Italian Game: Knight Attack, Ulvestad Variation that the only good move for white is 6. Bf1!, going back to square one. Some questions arise:

• Isn't the player of "going back to the original square" losing time?
• If "going back to the original square" is planned in the opening repertoire, why doesn't they shortcut the line, like not doing 2...Nc6 (with doing 9...Nb8, it could be a waste of 2 moves) in Ruy Lopez?

Some pieces are better positioned in different places at different times. Especially in closed, maneuvering positions, it doesn't matter as much that you move the same piece twice as it can't be exploited. The knight serves one role on c6 at the start. It defends the pawn and covers d4. As the situation has changed, it doesn't need to be there and can be relocated to serve another role.

In this case it allows c5 to be played and Bb7 when it doesn't block the bishop's diagonal.

If black were to immediately play d6-Nd7 then it would be the Philidor and this allows white other options to adapt to black's move order.

White has also spent moves on the bishop. On b5, it threatened to capture the knight and win e5, in some scenarios, so black had to adapt their setup to that scenario. When black kicks the bishop with a6-b5, it is repositioned to a different diagonal. This is often the same diagonal as the Italian bishop. The advantage of this move order is that black can no longer play d5 with tempo on the bishop and white has provoked pawn pushes on the queenside which may become weaknesses.

We can consider this in the context of the King's Indian.

1. At first, black plays Nf6 to cover e4.
2. Later, black allows white to play e4 but by that point, black is ready to castle.
3. White plays Nf3 supporting the central e5-d4 squares. After black plays e5 and white castles, if black captures on d4, white can recapture with the knight.
4. Black plays Nc6, attacking d4 (and black would also win e4 after some tactical sequence). This provokes d4-d5 so the knight moves back to e7. The knight can be more aggressively positioned here as it doesn't interfere with the other knight.
5. White retreats the knight to e1 to play f3 and relocate the knight to d3 where it supports c4-c5. The centre is now closed so it's no longer needed to guard d4.
6. Black retreats the f6 knight to d7 to allow f5 to be played. On d7 it also covers c5.

If black starts with f5 then it's, of course, the Dutch Defence. This allows white other options to maybe try to exploit the weakness of starting with this move. That is, it opens the king's diagonal while black still hasn't developed and castled.

The player retreating is losing time, yes, but in almost all cases the retreating move is either after successfully forcing an overextending move (such as in the Ulvestaad and the Alekhine's) or after enough pieces have been developed and the position is closed enough that time stops mattering as much, as neither side can break through fast enough to punish the "wasted tempi".

2... d6 is the only other playable move to defend the pawn on e5, but the Philidor is not reputable. For good reason too. White gets some nice positions. If you're planning to play the Ruy Lopez and planning to hit 1500, I'd recommend learning lines against the Philidor now rather than later. There's less theory, but it's rather common. I can show a few lines here:

In the Ruy Lopez, the main positional struggle is with the e-pawns for both colors. The point of the Breyer is to maneuver it to d7 to protect the e5-pawn. Here is one illustrative game showcasing the idea

I got this from Mastering the Spanish which was recommended by @pfren. Talks all about structures in the Ruy if you are interested