Fianchetto bishops

A fianchettoed Bishop is not automatically good.  It can be good, bad, or overrated.

Good - A prime example of this is the main line of the Benko Gambit accepted where it, combined with the Queen and Rooks, can become a powerful attack on the b2 pawn and a1 Rook

Bad - In the Kings Indian Defense, Mar Del Plata, the fianchettoed, dark-squared Bishop is actually Black's Bad Bishop.  An endgame of this Bishop against a White Knight will usually be lost for Black.

Overrated - In the line of the Alekhine Exchange Variation with 5...cxd6 where White plays Be3, Rc1, and b3, the Bishop on g7 is overrated.  It is nice and open, but it whiffs as it hits nothing.  It looks good but it is easy for White to work around.

So fianchettoed Bishops are not always great.  It depends on the specific situation at hand.

A Bishop on a long diagonal can be good, bad, or overrated, like the good, the bad, and the ugly!

when the opponent tries to trade the fianchettoed bishop it is because either he recognizes that the said piece is the best minor piece relative to the other ones, and therefore if it  leaves the board, the position should at least lose some dynamic potential.

or he recognizes that he may be able to use the weakened squares being guarded by that bishop, usually in order to attack the castled king there. there are other motives, but these two are the most common to my knowledge.

when fianchettoing the bishop, personally i am relying on the potential strength of this piece later in the game and not necessarily immediately. even if there are many pawns in the center, for as long as the pawn structure is not completely closed, or in other words can still be opened at any point, there is still that potential for the fianchettoed bishop to become stronger.

the other upside of fianchettoing as opposed to developing the bishop in a straightforward manner, is it is less exposed to harassment, especially from pawns.

for the last part, being able to control two diagonals means very little if most of the squares on those two diagonals are not important to the game, if not on the long term, then at least over a number of moves. on the other hand a fianchettoed bishop will always exert influence over two key central squares which are definitely important all throughout the game. there are of course exceptions. that's what makes the game interesting.

Combine what is said here in post 3 quoted above and combine it with post 2 and you see why White often tries to trade the Fianchettoed Bishop in the Dragon and Closed Sicilian, but almost never in the Kings Indian Mar Del Plata.