Why do landing gear bays in commercial aircraft not have a fire extinguishing system?
Cost/Weight/Complexity, the usual reasons why you avoid to add another systems. But let's analyse if you really need it.
Easy to prevent
From the data of this Boeing document:

at least 62% of the wheel well fires are caused by applying excessive grease
at least 11% of the wheel well fires are caused by hydraulic leaks
at least 3%  of the wheel well fires are caused by incorrect application of solvents

From the fire protection standpoint the landing gear is a quite simple device: maintenance staff should pay attention where and how much grease they put, pay attention where solvents are put, and the only flammable liquid is the hydraulic fluid. An engine is much more complex, you have many flammable fluids (fuel, hyd, oil), many pipes and extreme forces, which make the maintenance error and engine damage more probable. Then, causes can also be external (like bird strikes). This makes an engine fire event probability much more higher.
Moreover, most of all events of wheel well fires appear after landing (i.e., after braking), which is still a serious problem, but not as serious like in-air fire.
Rare
Wheel well fire are 10x less probable than engine fires and 1.5x less probable than APU (source):

There were only 2 fatal accidents related to wheel well fires: Propair Flight 420
 and the Nigeria Airways Flight 2120. In both cases pilots were unaware of the fire and they didn't take any countermeasure.
Easy to solve
Just put the landing gear down. The &gt;= 200 kts air does the rest. If it doesn't work, at least the most flammable materials (rubber, hyd pipes) and the heat source are now outside the aircraft frame and it will take more time to reach the wheel well, so you have more time to land.
Since wheel well fires are caused by high brake temperatures, the procedure is even usually applied before the fire actually exists. For example, the HOT BRAKES procedure of Airbus requires to lower the landing gear (and turn on the brake fan, if available) as soon as the brakes become overheated, potentially preventing in this way the fire event.