Given that 1.d4 is said to produce better results than 1.e4 and about half of all 1.e4 games involve the Sicilian Defense, could a simple idea like avoiding trading the d pawn for black's c pawn in the Sicilian be used to produce better 1.e4 results? Perhaps after 20 or 30 moves the d pawn will come in handy after all!
If you're strong at tactics, after you've played 1.e4, playing an early d4 to open up the game puts the burden of defense on Black to defend against these. Generally when you've played 1.e4 in an opening, your goal should be an early if sound d4 as well. The same is true for Black after 1..., e5, i.e. to seek an early ..., d5 when sound. Playing a Closed Sicilian gives Black more time to build up a defense. And since Black generally plays a lot of early pawn moves in the Sicilian, that also gives White a time advantage which he can try to exploit tactically by an early opening-up of the game. But as someone else has pointed out that Larsen had claimed, the standard "d" pawn for "c" pawn trade is giving up a center pawn for a less valuable off-center pawn, which can be positionally suspect. If you're well versed in the Sicilian lines and good at tactics, playing the standard early follow-up d4 would still seem to me to be the better course of action though. Conversely, the Closed Sicilian may be better suited to someone who is not as strong tactically but plays a strong positional game.
All the main lines against the Sicilian are the open Sicilian. This opening of the center gives white better attacking chances against black's lack of development.
Larsen claims that playing d4 is a positional mistake, allowing black to exchange a less valuable wing pawn for a center pawn.
Spassky played the closed Sicilian with great results. And there are many anti-Sicilians which claims to give white the advantage. The Grand Prix is the most fun, but I personally prefer the KIA.
The main difference between the open and closed Sicilians is the number of moves before the attacking begins. The open offers more tactics right from the start. The closed allows both players to finish developing before any attack really develops.
The real answer is that neither is necessarily good for white. Since every line of the Sicilian is so heavily analyzed, the advantage goes to the player with the better knowledge and comfort in the positions.
You are certainly far from being the first person to raise the question. Alekhine, in his Collected Games, recommends in the notes to one game that White should play 3.Be2, but in all of his other games he actually plays 3.d4. There is a book called the Chameleon Sicilian by Andy Soltis that points to certain advantages of 2.Ne2, retaining the options of d3 or d4 depending on how Black responds. For example, if Black expects d3, and combines ..e6 with ..g6, then d4 becomes very strong. On the other hand, if ..d6, then d3 leads into lines where Black usually goes for ..d5.
One of the remarkable things about Chess is the balance inherent in the initial position. Typically White keeps a small but tangible advantage ("normal opening advantage") for about 20 moves, and nothing much has ever changed that. One could define the statistically best moves but in practice psychological comfort is more important. (and high winning percentages sometimes attach to the moves that strong players adopt versus weak opponents.)
As has been pointed out, avoiding d4 can cut down on the amount of book learning that is needed, but that cuts both ways. Strong Sicilian players just need to know one good reply to each of Whites offbeat attempts.
If you see in Chessgames.com then you can see the below openings e4 c5 Nf3 d6 which is pure Sicilian Najdorf in the Opening Explorer then you would be seeing the winning percentages of White Najdorf Winning Percentage
Now you can see that with d4,c3,Nc3,Bc4 White has the maximum percentages win even though the most number of games are with d4 .
You can delay d4 if you find convenient for yourself and make some other move . What I feel is that you do not have a liking for Open Sicilian and want to deviate . So it is not a difficult choice either . There are other lines where different ideas also come into picture and honestly these Lines are easier to understand than open Sicilian .