Perhaps you’ve seen some power supplies labeled as “regulated.” Regulated power supplies add a voltage regulator and some hefty filtering capacitors, but some are better regulated than others. If they were designed for routers, cordless phones or battery chargers maybe a small AC ripple won’t matter.
For most guitar effects removing the AC ripple is essential. The power supply needs to maintain a steady voltage output and deliver enough current to power everything it’s plugged into. (Most pedals have current requirements marked in milliamps on the back or in the manual.)
Designing a compact power supply that delivers a ton of current is easy if you don’t mind some AC ripple. Regulated power supply designs are straightforward as well, but they deliver less current, require a few extra parts and some hefty filtering capacitors. Designing a power supply that does both is more challenging and not something you’ll find for $6.99.
Overloading the power supply can be a source of noise, but this is rarely the problem. Inexpensive imported power supplies are often rated for 2000 milliamps or more. Even power thirsty pedals rarely require more than 100 milliamps.