Gain and level controls on an amplifier-a good thing?

I think it depends on the level of sound quality you are going for. If it is the highest you can achieve, always leave unnecessary controls behind. They add signal path and lower the fidelity. This is why audiophile level equipment generally have one button and no potentiometers. On/off.

But, If you have high gain noise they are a lifesaver.

Do you mean they have independent gain and level controls, or are you calling them the same thing??

A gain control on a preamp can be really great, since most have too much gain to be useful, and therefore too much noise. It could also change the character of the preamp considerably depending on the setting. 

A level control (simple variable resistor) on an amp can help with channel balance issues, it’s more of a convenience feature installers may like to see.

I had the controls on my Parasound HCA-1000a bypassed and it sounded better...