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A light airplane often cruises at around 75% of maximum power.

Good point . . . I was probably thinking of larger, heavier, faster aircraft where cruise power is significantly lower than max power. As an extreme, I seem to recall that the Concorde cruised at about 20% power.

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Obviously I don't know anything about these sorts of things, but 20% power may have been all the engines were capable of producing with the much thinner air at cruising altitude.

I guess that depends on whether by power it's generally meant "the max power the engines are capable of under ideal circumstances" or "max capable under current circumstances". I think the latter is generally what is assumed when talking about operating (since it's hard to know the former). For example, in a car, you would probably assume that meant the gas pedal half depressed (and even that would be grossly wrong to the actual meaning of the latter interpretation, given gearing and the RPM power curve).

Jet engines actually perform better at higher altitudes, bypass and propeller notwithstanding.

No, they are more efficient at higher altitudes, mainly due to the colder intake air, but they have lower performance (as in maximum available thrust), due to the air density being lower and there being less available to burn the fuel.

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