Is it legal to use handheld radios to listen to aviation frequencies in the USA?
Your receiver must comply with USC 47 302a, the law that says, "you can't interfere with other equipment".

USC 47 301 in general is all about "transmission of energy", or broadcasting.
And it really is beyond the scope of government to say you can't stick a piece of metal in the air and process the signals it receives, provided you don't cause interference to anyone else.

Assuming your radio is receive-only, you really won't have a problem with that. (short of a total malfunction!).