Can I use a standard PC power supply to power a raspberry pi?

E.g. this one: http://www.amazon.com/iMicro-IM400W-ATX12V-Power-Supply/dp/B002HREGRM (or just take one from an old unused computer). Amazingly, these things are sold starting from 1$.

Most people seem to be looking for small and lightweight power sources, but since we are contemplating to build a PCR machine, size and weight are not an issue.

So far I only see advantages (but maybe that's because I don't really understand electronics):

- Lots of power (like 20-30 A): We are thinking about using a peltier element for heating and cooling (e.g. http://www.amazon.com/TEC1-12706-Thermoelectric-Peltier-Cooler-Volt/dp/B002UQQ3Q2). This one requires 12V and draws apparently up to 6A (and probably shouldn't be on the same circuit as the Pi, right?)
- Different Voltage outputs (3.3/5/12 Volts). 
- Lots of cables. So I'm thinking we just pluck a 5V cable for the Pi, and a 12V cable for the heating element (right?).
- Nice on/off switch
- Nice casing
- Nice inbuilt fan

Any reason why this wouldn't work?