Having flown the B737, and several of its variants, and been an FE on the
727, brake energy is a consideration. Long runways reduce that need, however
short runways with heavy load factors can overheat the brakes. The problem
can surface in two places. One is on the ground, and the explosion can kill
those nearby. The other problem is in the air and happens some 20 mins after
takeoff. The accumulated heat can, and has, caused a wheel well explosion.
In particular a B727 over Mexico a number of years back. There is a brake
energy chart, and for most slow turn arounds, it is usually a non issue.
Short runways, heavy loads, and quick turnarounds raises the risk.
Additionally, the other points that have been made about parts, weight, and
so on are also valid. BTW the A320 et al series also have brake cooling
fans, however they are only used over a certain temperature. Leaving the
gear down after takeoff is not an option for cooling the brakes. The brake
energy chart is what is followed. Leaving the gear down after takeoff (and
it is done sometimes) to cools the wheels violates the takeoff criteria.
With the gear down the aircraft does not meet the climb gradients on an
engine failure.

I would suggest that there is probably no one single reason the 737 has
exposed main wheels, but many. And probably Boeing has some idea what it is
doing.

Simon