still-learnin said:
. . . almost every outlet the device that you will be plugging in will have a cord with a #14 or smaller wire. . . but an 8 inch #14 pigtail is a violation.
It's a fair question. Let me address the vacuum cleaner's power cord first.
The whole intent of establishing ampacity limits and using overcurrent devices to make sure current does not exceed the ampacity limits has to do with protecting the conductors' insulation system from damage. Too much current will raise the temperature of the metal conductors to the point that the insulation starts to degrade, or even to melt. That, in turn, will lead to short circuits and possibly to fires. Anytime you ever get into discussions about ampacity, you should take a moment to remind yourself of this reason for ampacity limits. It will help you stay on track, for the rest of your discussion.
But how much current is too much? It depends on many things. One key factor is the manner in which the conductor is routed. Another is the environmental conditions surrounding the conductor, or more if applicable, surrounding the conduit. If the conduit runs through a hot area, then you can start to see damage to the insulation at a lower current level. If there are other current-carrying conductors in the same conduit, then each will feel the heat being released by the others, and here again you can start to see damage to the insulation at a lower current level. That is why there are derating factors for temperature and for multiple conductors in the same conduit.
A vacuum cleaner's power cord is not surrounded by conduit, it is used in rooms that are not too hot for the occupant, and it does not share a limited space with other conductors. It is run in free air. Therefore, it can give up its heat to the surrounding air more easily than a #14 sitting inside a conduit that is inside a wall. So it should seem reasonable that a #14 appliance power cord can take every bit of the 20 amps a breaker can supply, and not be a risk of damage.
Please note that I could have just said that the vacuum cleaner's power cord is not covered by the NEC, and left it there. But you asked for more informative responses.
Finally, I will address your question about using 8 inches worth of #14 at the outlet box. You really cannot count on the owner to use appliances drawing less than 15 amps. The owner will plug in anything that looks like it has the right kind of plug, and will never worry about the possible results. They will even plug in something that draws 21 or 23 or 25 amps. All they know is that that is a receptacle, and this is a plug, so they ought to be able to just plug it in. Please take note that a 20 amp breaker might not trip on a 21 amp load. It might trip on a 25 amp load, but it might take a while. What we want to prevent is insulation damage to the #14 wire on a sustained load higher than 15 amps. So if there are #14 pigtails (other than in circumstances specifically described in the code), you have to protect them with a 15 amp breaker. If you want a 20 amp circuit, then you have to make sure all conductors can safely handle 20 amps or more for a sustained time period.
Short answer: just think of it as an added safety precaution.
