The taps mentioned in 210.19 are not the same thing as the tap mentioned in the OP of this thread. Those taps are fixed loads such as ranges, ovens, cooktops, or taps off lighting circuits to individual luminaires, all of which are permitted to tap off the circuit that supplies them without additional overcurrent protection. The condition of what the OP is asking about is reducing overcurrent protection on an extended smaller conductor from the original circuit. It is similar condition to feeder taps mentioned in 240.21.
The circuit the OP was attempting to tap is a BRANCH CIRCUIT. Branch circuit taps are addressed in 210.19. Any tap from a branch circuit MUST comply with 210.19.
240.21(B) says "conductors shall be permitted to by tapped, without overcurrent protection at the to a FEEDER..." The circuit in the OP is not a feeder. 240.21(B) does not apply to a tap from a branch circuit.
I do not disagree with the definition of feeder or branch circuit. If the circuit meets some of the conditions of both I don't see how you can say it is impossible to be both, it is just a situation we do not have an official name for. It is definately not entirely one or the other on the 30 amp portion of the circuit. The 15 or 20 amp portion does fit definition of branch circuit.
These two statements in red are contradictory. If you agree that a feeder is all of the circuit conductors between the service equipment and the final BRANCH CIRCUIT ocpd, and you agree that a branch circuit is the circuit conductors between the final BRANCH CIRCUIT ocpd and the outlets, then you cannot believe that a circuit can be both. A circuit cannot be "before the branch circuit OCPD and "after" the branch circuit at the same time. If the 15 or 20 amp portion fits the definition of a branch circuit, then the conductors before the 15 or 20A ocpd fit the definition of "feeder."
Overcurrent protection rules for the conductors and for the receptacles have not been broken, so I don't see any real danger. I am not suggesting it is a good design practice but see no code violation either.
Put it this way - I don't see where there is a requirement that receptacles, luminaires, or other loads are required to be on a branch circuit, but rather the conductors supplying those items by definition become branch circuit conductors - usually.
Overcurrent protection is found in Article 240. Article 210 applies to Branch Circuits. Article 215 applies to Feeders. Branch Circuit and Feeders must comply with 210 and 215 respectively, as well as 240. "Outlets" are only found in Art. 210, not in Article 215. The definitions say that outlets can only be connect to branch circuits. The requirements that receptacle OUTLETS, luminaire OUTLETS, or other load OUTLETS be on branch circuits are found in Art. 210 and in the definition of branch circuit.
Lets try this. I've pointed out in Art. 210 where is talks about Outlets (210.21) and the definition of "Branch Circuit" which mentions Outlets. Can you point out anywhere in Art. 215 or the definition of "Feeder" where it mentions connection Outlets to a feeder?