I think you are expecting too much from a cheap industrial amp designed for rock bands. The S/N is not adequate. Also the input trim sensitivity is obviously done on the cheap. It must be a standard old fashioned and cheap input trim. If on the other hand it had an opamp, with the input sensitivity set in the input loop, then S/N would not be effected by the input control.
In a large auditorium with lots of noise and live bands, your issue would not be noticed.
So as I suspect that Crown amps are probably acceptable for sub duty but nothing else in a good domestic system.
You are right about Audyssey though. That is a dreadful quality spoiler and I do not recommend it.