Can I power a laser directly from a computer PSU?
As JRE wrote in a comment: No, you should not drive the laser directly from the computer PSU.


  Computer electronics are very sensitive, so the PSU must have a nice, clean and smooth 12V output right?


The first part is mostly correct, computer electronics are very sensitive, but your motherboard and GPU probably has dozens of high quality low voltage regulators on board, to convert the 12 volts down to 100 amperes of a various mix of voltages in the order of 1-3 volts or even sub-volts. Nothing these days are driven directly by the 12 volt line except the fans and possibly USB3 in one of the fast charging mode.

This means that the 12 volt output does not have to be very stable at all. The regulators are able to handle an input variation of several volts up or down.