The biggest problem with PSUs is quality: a high-end single-GPU PC usually draws 350-400W peak measured at the wall while a typical entry-level PC draws less than 250W so almost any PSU on the market will usually be fine in terms of power rating.
The problem with low-quality PSUs is that they tend to fail prematurely even under light loads or simply fail to work correctly altogether. They also have a tendency to kill other components more often than better-quality PSUs do when something goes wrong.