At 365chess.com, 1.c3 is ranked as the 14th most common first move for white. If the Caro-Kann defense is considered as a sound defense, why is the Saragossa opening so rare for white? After all, white is preparing to play 2. d4 in the next move and transfer into some solid defense systems. For example, one possible line is
Another possible line is
A black defense and its white mirror counterpart will often play out quite differently (compare the rather sharp Sicilian Defense and the rather quiet English Opening).
The right to move matters, in both ways. By moving, you give away information to your opponent - the set of variations you can choose from shrinks with every opening move. Early moves are usually played to either proactively increase your control over the board or reactively counter your opponent's moves (the best moves do both). This second category of moves only make sense as answer to one of the first category: If your opponent doesn't play a move that you have to react to, you'd want to play a move to advance your own plan rather than a "counter" to a plan your opponent has not committed to yet. Commitment is an important factor here. If you parry right before knowing which side your opponent will commit to, they can now simply swing left and catch you off-balance. Even if they cannot immediately strike that way, you will still have wasted time you could have used for more useful moves. The further in advance your opponent knows what setup you are heading for, the easier it is for them to screw your plan.
Most openings are a series of moves reacting to each other. Simply playing a "reversed" opening won't lead to the same result because the dynamics can be totally different depending on who strikes first.
The Caro-Kann defense strategically centers around the d5 square. Playing 1...c6 merely is a means to the end of playing 2...d5 next turn and being able to take back on d5 with a pawn if White plays exd5. Playing 1...d5 right away is certainly possible (leading to the Scandinavian Defense), but then Black concedes that he has to take back on d5 with a piece, when he will obtain a half open d- instead of c-file (generally speaking, a half-open c-file and two center pawns are more desirable than a half-open d-file and only one center pawn). Of course, White can refuse to take on d5, but that's the idea.
Now, let's have a look at the same idea, but from the white side. Sure, White can play 1.c3 to prepare 2.d4. But since Black obviously did not have time to play ...e5 yet, this is simply not necessary and White can play 1.d4 right away! Now Black won't even be able to play ...e5 with ease (the best moves: activity as well as prevention). Isn't preventing the black pawn from entering e5 not much better than preparing to attack it with 1.c3 after the fact? And remember, Black did not commit to this pawn move yet anyways and may answer 1.c3 with a completely different move, leaving White look rather silly for preparing against something that may never happen.
On the other hand, if Black does not play ...e5, White doesn't actually have to defend d4 by playing c3 ... and the c-pawn is free to be moved to c4, from where it attacks d5. If it now gets traded for Black's d-pawn, we may actually arrive at a similar situation as in the Caro-Kann exchange variation: White has pawns on both central files and a half-open c-file.
To no surprise (and in contrast to 1.c3), 1. d4 2. c4 is one of the most popular ways to open the game as White of all time. So why not go for a Queen's Gambit if you like the Caro-Kann?
1. c3 (and 1. d3 and 1. e3, which can lead to reversed Pircs, French defense or QGD) aren't bad in that they give White a worse position. So those moves might have some merit as a surprise weapon (if you don't do it too often). But they do offer Black the advantage of setting the first foot in the center and the possibility to defend it, which is normally White's role in the game.
Another question which you should ask yourself: why does Black play c6 in the openings you mentioned? In the Caro-Kann, Black needs to play c6 in order to be able to play d5 (and not having to take back with the queen). In the Slav, the pawn is already on d5 but the idea is the same: Black wants to keep a pawn on d5, thereby establishing a bit of control in the center. For White, this isn't necessary; he can just put a pawn on d4 and play c3 only if it's under attack (e.g. in the Colle system).
Looking at it from another angle: in the two examples you mention, if you're going to play 2. d4 anyway, why not play it on the first move? If your opponent doesn't respond with 1... d5, you have more options. For example, suppose (s)he plays 1... f5; I think the pawn is actually worse on c3 than on c2, since it blocks the natural development of the queen's knight and a possible fianchetto of the queen's bishop (in the Leningrad variation).
Because White has the initiative and usually feels that s/he can do better than "a sound/solid defense".
c3 is an inferior first move. White has the advantage of moving first and should use it to seize the initiative and put black on the defensive. The basic idea behind the Caro Kann is to counterattack in the center with d5 after white plays d4 without blocking the light-squared bishop as in the French.
The key word here is "counterattack." White should not be looking to counterattack at this stage. As the first player, white should be putting black under pressure and forcing black to respond to threats like dominating the center. 1. c3 is more of a defensive move and it just doesn't make sense for white to play defensively on the first move of the game.
