Right. Using the 10 times example, a load drawing 10A at 12V through a 10:1 transformer will draw 1A @ 120V. The power (120 watts) is the same on both sides.
Of course, there is some loss so it's not exactly 100%, but it is relatively small and not considered for sake of discussion to make the point. Generally, an audio amp has much lower overall efficiency than simply considering a transformer so, yeah, power available on the output side will always be meaningfully less than on the input side, until we have superconducting amps then it won't be much of a factor to consider.
Just because there is a knob doesn't mean you should turn it.