Listen to Sixty Fiver, you want to keep a front brake on all bikes for safety and better performance.

Coaster brakes are drum brakes and they will pretty much last forever if you maintain your bike.
They aren't affected by weather, so don't lose performance in rain/snow etc.
Using one the back with a rim brake on the front will put even less wear on the coaster brake, as your front wheel will do most of the braking.
On that note, coaster brakes were not intended for higher speeds, and they fade under the heavy load, which is why rim brakes became standard. Again, you want that front brake.
I have seen a coaster brake that locked up internally because of a problem with the chain, and the lever arm was not held tight against the chainstay.
A replacement will only set you back about $25 if you ever need one.