Have the section of the NEC for that?
How does nearly every low power appliance plugged into a 20 amp circuit plugged into a 5-15p work with that?
Any appliance with a 5-15P plug is designed to be protected by a 15A or 20A breaker. That doesn't mean you can chop the plug off, install a 5-30P on the appliance, plug it into a 5-30 receptacle, and expect it to be fine and safe. Similarly, the OP cannot chop the plug off the compressor and install any other plug to match an existing receptacle.
The breaker protects the wiring in the wall AND receptacles (if any are installed). 210.21(B)(1) Single receptacle on an individual branch circuit: A single receptacle installed on an individual branch circuit shall have an ampere rating not less than that of the branch circuit.
So if he replaces the receptacle with a 30A receptacle (for example), the breaker cannot be greater than 30A. I didn't find anything specifically that prohibits installing a receptacle larger than the breaker though (ex. a 50A receptacle with a 30A breaker). Maybe there's language somewhere in the code that says it.
430.109(F) Cord and plug connected motors: For a cord and plug connected motor, a horsepower-rated attachment plug and receptacle...having ratings not less than the motor ratings shall be permitted to serve as the disconnecting means.
430.110(A): The disconnecting means for motor circuits rated 1000V nominal, or less shall have a current rating not less than 115% of the full-load current rating of the motor.
So, assuming this is a 3 HP motor, which has an FLA of 17A, means the receptacle has to be at least a 20A receptacle (rated for at least 3 HP) (17 * 1.15 = 19.55 A). But if he uses a 20A receptacle, he'd have to use a 20A breaker to comply with 210.21(B)(1).
The conductors need to have an ampacity of at least 21.25A (
430.22): 17A * 1.25 = 21.25A. So that means at least #10 NM-b, or #12 THWN in conduit. That doesn't have much bearing on breaker size or receptacle size, though.
Table 430.52(C)(1) says he can use UP TO a 50A breaker, BUT 210.21(B)(1) again says he'd need a 50A receptacle in that case.
Theoretically, he could install #10 NM-b wire, a 50A breaker, and a 50A receptacle, even though #10 can't handle 50A. 240.4 says that "conductors...shall be protected against overcurrent in accordance with their ampacities specified in 310.14, unless otherwise permitted or required in 240.4(A) through (H)." And 240.4(G) refers you to Article 430 for motor circuits, which allows you to oversize overcurrent protection, and doesn't mention anything about overcurrent protection being different if you're using a cord and receptacle.
I think it becomes a gray area when it's a receptacle that someone can plug any appliance (with the corresponding plug) into. #10 on a 50A breaker is fine on a motor circuit, but if someone plugs something else into it, it's no longer a motor circuit and 240.4(G) no longer applies.
If this were my compressor, I'd install a 30A breaker, and either hardwire an A/C disconnect next to the compressor, or install a 6-30 receptacle and plug, run either #10 NM-b wire or #12 THWN (if hardwiring) or #10 THWN (if using a receptacle, just to be on the safe side), and call it a day.