The biggest problem with such a supply is the fact that without modification (not an easy task unless you have a schematic for the supply and are an "expert" in power supply design) you can't set a current limit for a given voltage.
Let's say you have a 5V circuit you are testing out, that you believe (based on your calculations) will only consume 100 mA of current when running, and you don't know there's a short in it. With a good quality bench PSU, you can set a current limit (and a voltage limit, if desired) to say "regulate the output at 5 volts, 100 mA".
If you hooked up your circuit to such a PSU - and turned it on, the over-current indicator would flash (or there would be a tone, or something else), and the current flow would be interrupted; this would happen so quick that there would likely be no damage to your circuit.
Now let's say you hooked the same circuit up to you modified PC power supply: The 5 volt rail of such supplies usually can pump at several 10s of amps. If you are lucky, your circuit fries and perhaps one of the wires goes up in a puff of smoke, a bright flash, and maybe a loud "bang" as it vaporizes (been there, done that - fortunately, it was with a homemade motor, and not anything I really cared about). If you are unlucky - well, you have a small fire on your hands, and you better hope you have a way at hand to put it out quickly...
Now, you could possibly homebrew a small PCB with a few linear regulators and such on it, that you could plug into the output of the power supply that could do current regulation (and be adjustable) - for about an amp or so of output. You could even add voltage regulation to the mix. At that point, though, you are well on your way to building a simple bench power supply...