Why do exterior decks not use 2x12 or 2x10 lumber?
There’s many reasons: 1) twisting, 2) cupping, 3) aesthetics.

A larger board will twist more than a smaller board will as it dries out. As it dries out, the grain will shrink and a larger board will have a larger variety of different sized grain throughout (across) the board. This will cause the size of the gap between boards to shrink and enlarge as it dries out. This will be unsightly.

As the boards are installed, the boards will need to be inspected (looking at the end grain at the end of the boards) so the grain is installed with the curve downward. With a large board, the grain at the end of the board will be more of a “S” rather than a “C” (that can be turned downward). This will allow part of the board to cup and collect and hold moisture, which will cause rot, etc.

Seeing a large board laying flat is a bit unusual. Yes, because a smaller board is more customary it’s more aesthetically pleasing.