Yeah rated amps is at rated hp output. A synchronous motor won't exceed the rpm implied by the number of poles and the frequency of the current delivered. Nor will an induction motor which induces an excitation current in the rotor, but still relies upon phase rotation and will have slippage.
I don't think you would want the motor running at it's Max or close to it all the time. I'm sure some electric motor guy will chime in here soon that will know for sure.
If its rated that way, I don't see the issue. That's probably the most efficient way to operate, to match an actual load to the nameplate. Of course it rarely perfectly works out that way, so reducing the motor's duty cycle, or alternatively, using a VFD to alter the (induction) motor's output can be on the table.