Why is the Open Sicilian even played?

Of course that's the point. Pure gambits have a point too. They too are partially unsound

@LloydThompson said in #21:

Of course that's the point. Pure gambits have a point too. They too are partially unsound
Open sicilian is completely sound according to current theory, thats the difference

Glad we agree so completely

@Fenamer said in #1:

The open Sicilian breaks a lot of important opening principles, like wasting a tempo by allowing black to do smth after Nxd4, opening the centre before castling, trading a center pawn for a side center pawn, delaying castling, like what is this? is this a strategic opening trap?

Yeah, a cheap trick. Bent Larsen

Stean, Simple Chess, 1978 or something linke that:

Minority attacks derive from the Pawn structure, Pawn structures derive from the opening. Go back to the eras of Capablanca and Alekhine and you will see Queen's Gambits, hoards of them, with hoards of minority attacks descending from them. Nowadays [1978; still relevant] the Sicilian Defense is all the rage. Sicilians here, Sicilians there, Sicilians absolutely everywhere. Why this saturation with Sicilians? Does the Mafia's influence really extend this far? The answer lies in the minority attack. The whole idea of the Sicilian is for Black to trade his c Pawn for the d Pawn. White almost invariably obliges: 1.e4 c5 2.Nf3 Nc6 (or d6 or e6 or g6) 3.d4 cxd4, when Black immediately arrives at a minority attack Pawn structure. Half-open c file, extra central pawn, 2-3 minority on the Queenside; these are all the necessary ingredients. Sounds infallible, so where's the snag? Why doesn't Black win every game? The problem is of course that White has a lead in development in the early stages, which may prove difficult to survive. Black's prospects lie later in the game when the winds of White's initiative have blown themselves out."
The structural weaknesses White accepts because he is trying to avoid Black's plan to launch a minority attack to get a winning endgame and must attack. They are not the cause of Black having winning endgames (otherwise White wouldn't weaken his position in such a way); merely they are a symptom of him having to attack the Black King. The root cause of this is the minority attack, and this is why most Sicilian endgames are winning for him. The minority attack is also a theme in any Rook endgames, so it's not just a late middlegame idea.

"... In the middlegame and especially the endgame you can get a long way through relying on general principles and the calculation of variations; in the opening you can go very wrong very quickly if you don't know what ideas have worked and what haven't in the past. It has taken hundreds of years of trial and error by great minds like Alekhine and, in our day, Kasparov to reach our current knowledge of the openings. ..." - GM Neil McDonald (2001)
Alexander McDonnell vs Louis Charles Mahe De La Bourdonnais game (1834): 1 e4 c5 2 f4 e6 3 Nf3 d5 4 e5 Nc6 5 c3 f6 6 Na3 Nh6 7 Nc2 Be7 8 d4 O-O 9 Bd3 c4 etc.
https://www.chessgames.com/perl/chessgame?gid=1261709
"... There is no doubt in my mind that if you really want to test the Sicilian then you have to play the main lines of the Open Sicilian. The problem is that there are just so many of them ... and keeping up with developments in all of them is a substantial task. ... as you become older, with other demands on your time (family, job, etc.) then it becomes more and more difficult to keep up with everything. At this stage it may make sense to reduce your theoretical overhead by adopting one of the 'lesser' lines against the Sicilian: 2 c3, or the Closed Sicilian, or lines with Bb5. ..." - GM John Nunn in part of a 2005 book where he discussed a 1994 game in which he had played 2 c3.

@Fenamer said in #13:

... why does unprincipled stuff work?
"I would caution you that this and other maxims are not to be blindly followed. In chess, as in life, rules must often be swept aside." - Chernev (1957)

Open D-file means open queen. You can often play Qd5 for some sort of double attack.

No, you are being too formal with your definition of the rules. You can say it is a half gambit; offering the center for one move, something like a positional sacrifice but only temporary. Black can bring its queen out fast this brings the center back equal, the difference is black is using pieces not pawns. Just like any gambit, it is not what you might think correct but if things go right for Black it will have more movement of its pieces and an active queen that is not at risk.

@Fenamer said in #9:

... To my understanding: White's knight went from g1 to d4. black's
pawn went from c7 to ??? Each one cost 2 moves. but at the end of the
sequence, it is black to move. I think black has gained a tempo here.
Has Black gained a tempo after 1 e4 e5 2 Nf3 Nc6 3 Bc4 ?
@Fenamer said in #9:
If white had played Nc3, he would have 2 pieces to 0 pieces. ...
But no progress would have been made for the c1-bishop.
@Fenamer said in #13:
... So basically, learning theory is easier than learning
the exceptions of breaking opening principles. ...
I have not seen a new edition of Modern Chess Openings since 2008.
@Fenamer said in #5:
... and there is no 'initiative'. If white was offered
initiative, then no one would be playing the siclian.
"... If White plays passively or his initiative runs out of steam, then typically it's Black, with the better pawn structure, who enjoys the long-term chances. ..." - GM John Emms (2009)