Alapin sicilian allows black to play d5?

Isn't a large part of the plan vs the sicilian defense to make it hard for black to play d5 by castling long and controlling d5 with the knight, queen and rook?

While in the alapin you allow black to play d5 early by:

1. e4 c5
2. c3 d5

What's the theme/idea behind the alapin?

Not an expert on the alapin sicilian, but here are my take on the main ideas:

I personally believe that the Nf6 line is far more testing for black.

What highly favourable pawn structure, and the uncastled king doesn't matter too much in the endgame. Anyway Carlsen and other strong players went on to win the endgame for black after 10...Ne4. Probably only meant was better endgame player but don't think black has much to worry about in resulting position.

If I knew my opponent would play into the Qxd8 Kxd8 line, I would gladly throw away my sicilian repertoire as white and play this every time. That does not mean I think I have a winning edge as white, nor that I can beat any GMs with it. However, I think I would play for a win against most sub 2100 players.

@1

"What's the theme/idea behind the alapin?"
The idea is this. In the Sicilian by playing 1 e4 c5, black prevents d4 in the sense that white can only play d4 if white consents in trading his central pawn d4 for black's wing pawn c5, which gives black a long term endgame advantage. By playing 2 c3 white prepares to play 3 d4 where white can recapture cxd4.
The late GM Sveshnikov believed 2 c3 superior to 2 Nf3 and 3 d4.
The disadvantage of 2 c3 is that it obstructs the natural square for Nb1, so black can play 2...d5 or 2...Nf6.
Another main idea is that white does not fear an isolated queen's pawn in the spirit of Tarrasch.

The Alapin doesn’t make sense to me either. Black gets easy equality with 2… d5 and a slight advantage with 2… Nf6. 
Much better is 2. Nf3 d6 3. c3! with slight advantage to White.
Slightly better is 2. Nf3 e6 3. c3 if you know your opponent is a Taimanov or Kan player but a Barmen Alapin player, and you play the Advance Variation against the French Defense, as you’ll know more about whatever gets played than they do. Alternatively, if you play the KIA against the French, play it against the e6 Sicilian as well. 
Against 2. Nf3 Nc6, 3. Bb5 is best. Possibly even better than 3. d4.

@Etgann_Brollier, Black doesn't get advantage in any variation of the Alapin sicilian. That's nonsense.

I don't play the Alapin with white but I do play the Sicilian. (My lines)

The late GM Sveshnikov considered 2 c3 stronger that 2 Nf3.
https://www.chessgames.com/perl/chess.pl?yearcomp=exactly&year=&playercomp=white&pid=44139&player=&pid2=&player2=&movescomp=exactly&moves=&opening=B22&eco=&result=1-0

It is very odd seeing greats like Tal and Taimanov playing like beginners forgetting need to develop peices.