Artificially isolated pawn in the Caro-Kann I would like to know why it is so disadvantageous to have an advanced artificially isolated pawn when it can be exchanged by another pawn.
I refer to situations where a side cannot mantain such square with a pawn.

Examples:
In the Caro-Kann, after 1.e4 c6 2. e5 d6 3.exd6?!
What is so wrong with this last move?
Is it a matter of tempos (White lost two moves to go to e5 only to be exchanged ) or is there any more fundamental reason?
I know that the common thing to do for White is trying moving pawns to d4 (maybe f4, though it d be weakening).

Another example, for instance is when Black c pawn is on c5 (with a White pawn on d4) and then it is pushed to c4 before recommended. Then if White can play b3, Black tries to play b5, a6. Why not simply trade this pawn already?
The shortest explanation I can think of: if you play 1.e4 and 2.e5, presumably you want that pawn there for a reason. If you then immediately trade it off, you've lost whatever you were trying to achieve, like maybe space or central control.

In the case with ...c5-c4 followed by b2-b3: again presumably you want that pawn to be there for some reason (queenside space?). If instead you allow simply cxb3 axb3, then:


You don't have your pawn anymore
White has got rid of his a-pawn in return, rook pawns are least valuable pawns (can only capture one direction)
White has freed his a1 rook
White still has a single groups of pawns, while yours are split in the a/b pawn "island" and the c/d/e/f/g/h "island".


By adding ...b5/a4/a6/axb5/axb5/bxc4/bxc4 black also frees his rook and gets rid of the a and b pawns that could otherwise become weak later. And the c-pawn that you presumably wanted on c4 to gain space is still there.

However, I disagree that 3.exd6 is bad. White doesn't have good options there. After 1.e4 c6, 2.e5 is a bad move. It can't be maintained there and it doesn't help with the main goals in the opening (development, control of the center, and preventing the other side from achieving those).