So it's a bit tricky to categorize the INTENT of the NEC on this.
The NEC requires that a circuit be protected from over current and short circuit. An OCPD, such as a fuse or circuit breaker, does both tasks.
But the reason there is an entire section (Article 430) devoted to motor applications is because of the issue you raise; motor starting current can sometimes cause issues with the more generalized rules of OCPD sizing for other types of circuits. So does the NEC "discard" (by which I think you meant disregard) the motor starting current? No, in fact to a great extent that is WHY Article 430 exists. In table 430.52, you select the rating of the Branch Short Circuit and Ground Fault Protective Device. If you look at the values allowed in that table, they are far higher than you could use elsewhere, specifically because of the issue you mentioned.
But ALSO in that article, you are required to have RUNNING thermal overload protection for the motor, either in the form of an separate thermal overload relay, thermal devices inside of the motor, or you CAN use the OCPD if it provides thermal protection. Table 430.52 is based on a circuit where there is some OTHER form of acceptable running thermal overload (over current) protection in the circuit.
If you chose to do the latter, i.e. the motor has no internal thermal protection and you do not have a separate thermal OL relay, so you want the OCPD to do BOTH functions, that's where it can get tricky. If you follow the rules for thermal overload protection, you find that it requires the OCPD to be sized much smaller than what is allowed in table 430.52 (which by the way is the MAXIMUM size, not minimum). The problem is that most fuses or circuit breakers, when sized to do the thermal OL task, will NOT hold in if there is any kind of significant starting current surge, and you get nuisance clearing. THAT is not the concern of the NEC, that is the concern of whomever is getting cheap on trying to do two things with one device.
The NEC gives you a remedy, it's up to you to decide you want to take a chance at trying to squeak one by.
Side note from a pedantic engineer: "Inrush Current", despite the common use of it to describe motor STARTING current (aka "Locked Rotor Current"), is not the same. "Inrush Current" is a specifically defined term referring to the in-rush of current in an electromagnetic coil when first energized, where there is no impedance yet established. It only lasts for a fraction of a second, but is much much LARGER than typical motor "starting" current, in theory as high as 2200% of motor FLA. Inrush happens first, when there is nothing but the natural resistance of the winding conductors slowing down the rise of current, then once the coils begin to interact with each other and provide mutual induction to create impedance, the current drops down to what it take to create torque (in a motor), the "Starting Current", then stays at between 500 and 600% of FLA until the motor accelerates to around 80-90% speed. You get "Inrush Current" in transformer windings and solenoid coils as well, same issue. But in those cases, there is no "Starting Current" afterward.