What reasons exist for not designing airplanes with breakaway wings for crash safety?
I can't think of an accident scenario where this might help. If you're hitting the ground hard enough to crash but have survivors, you're looking at an accident like TK 1951, where not only was the wreckage all in pretty much the same area, but it didn't even catch on fire. Aviation fuel is not as volatile as movies make it seem. 

Maybe you are thinking of something like AF 358 which overran the end of the runway and burst into flames? Despite that fire everyone survived, but what if they realised it was going to overrun and jettisoned the wings whilst still on the runway? 

Well the biggest problem to me is how to slow the aircraft down without wings. At higher speeds, the wheel brakes are ineffective without the use of ground spoilers. Without the reverse thrust from the engines you are guaranteeing that the aircraft will be going faster when it leaves the runway, leading to a much higher chance of casualties. 

No piece of engineering is perfect either - what happens when it fails and the wings accidentally detach when everything is going well? What if they are flying in severe turbulence and the sensors detect high G forces and confuses that for a hard landing? Or if it a manual jettison, what if the pilots accidentally pull it, or a suicidal pilot does it while the other is looking the other way? 

There are many other problems too, such as how some aircraft are designed with the gear support in the wings, that some have large fuel tanks in the fuselage, and the extra weight and cost of getting such a system certified. Ultimately this suggestion falls into the same bucket as every other drastic safety idea - in trying to fix a problem that barely exists, it creates a lot more in its place.