I ride singlespeed freewheel. The advantages that I get out of having a freewheel are as follows:

1) You can corner fast and hard, without any concern at all about pedal strike. This is very handy in cases where you have to take sudden unexpected evasive maneuvers.
2) Go as fast as you want downhill. I've seen a lot of guys disengage from the pedals and rest their feet on the downtube on downhills, but the problem with that is if you have to brake hard suddenly, you're in a bad position: really hard to get your weight far enough back to brake hard (assuming a front brake), maintain balance and not go ass-over-teakettle.
3) Jumping curbs, giant potholes and other hazards is a lot easier at speed. It's not that you can't do this fixed, it's just way easier with a freewheel.
4) Generally, you can get away with a bit more gain in your drive train if that's your thing.
5) Generally, the ability to coast allows you to maintain a very quiet body in situations that require finesse (hard cornering, precise evasive maneuvering, hopping/landing obstacles, emergency braking where you must shift your weight behind the saddle.)

The disadvantages:

1) track standing at stop lights requires a bit more skill with a freewheel - particularly if you are stopped on a downhill, but you can do it.
2) I hear a lot of fixed riders talk about being more "one with the bike" this bears some water to my mind, but I also think that if you are doing a lot of coasting with a freewheel, you're probably geared way too low.
3) Some of your fixed gear friends will give you crap, although I haven't gotten much guff.

I think some fixed riding will probably result in becoming a better cyclist to some extent, but you can also become a better cyclist just by riding your bike. I have noticed that I tend to ride much faster than most fixed gear riders I see, though not all. I think the advantages of a freewheel open up that door.

As far as a freewheel going kaput goes: I've never had it happen, but I also ride with a White Industries freewheel, which is much higher quality than the average freewheel. I also don't ride dirt, which is harder on freewheels than street riding.