I disagree with your interpretation, the NEC doesn't say that, it leaves that to the listing which allows a 15 amp molded attachment plug suitable for a 15 or 20 amp circuit. 240.5(B)(4) says that if you make the cord in the field then the #16 gauge conductors are just fine on a 20 amp circuit so why should a manufactured cord be any different? You seem to be searching the NEC for some justification for your conclusion that doesn't exist.
I am not trying to interpret the NEC, I am trying to read it and follow it. I also am not trying to be argumentative, I am trying to learn.
The NEC says exactly what I stated - 2020 NEC 240.5(B)(3)
Extension Cord Sets "Flexible cord used in listed extension cord sets shall be considered to be protected when applied within the extension cord listing requirements." That is a fact, that is EXACTLY what the NEC says, not what I interpret it to say. Do you agree with that?
UL 817 (I have a copy of it) Table 114
Cord Ampacities and Voltage Ratings shows these type of cords to be rated at 13 amps up to 50 feet, and 10 amps over 50 feet. Do you have any disagreement with that (if so, provide the reference)?
The 16 AWG extension cord I have, the common type that anyone can purchase at Home Depot, is labeled at 13 amps (I can provide a photo if needed). That is a fact. Do you have any disagreement with that (if so, state your argument)?
The fact that the plug is rated at 15 amps has no impact on any of that. If it did, what if you put a NEMA 5-50R plug on it - would it then be rated at 50 amps? If you disagree with that please provide me with the NEC article reference to support your argument.
I know what 2020 NEC 240.5(B)(4) says - and it applies to field assembled cord sets, not to manufactured cord sets - which is the subject of this discussion here. Do you agree with that?
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I think the NEC is pretty clear. As Tom Baker said, I will look at when NEC 240.(B)(3) was added and the NFPA comments for that.