You can do what ever makes you happy, as for others they can do what the code allows and even though it may take them into other code article sections don't think they are somehow wasting time.Can somebody stop reciting every code article and just make a very simple response? You size your wire based on the over current protection device. There’s no need to get into the wires ampacity capability in 100 different situations. I have never looked at a piece of equipment and seen the amp rating but the looked at the lug rating to determine the wire amp rating to use. Quit over killing it if it’s 20a use #12 if it’s 30a use #10 if it’s 40a use #8 ect..
I've got one for you and will walk you through it. You have a 3 HP motor
? Table 430.148 gives a 3HP motor an full load current of 17 amps
? 430.22(A) requires conductors be sized at 125% of full load current
? 17 x 125% = 21.25 amps
? Table 310.16, #____ THHN 75 deg C column = ___ amps
? Table 430.52 allows up to 250% for the inverse time breaker
? 17 x 250% = ____ amps
? 240.6 states we can go UP to the next STANDARD size breaker
? you can use a _____ amp breaker and # ____ conductors