This comes down to the current rating of the actual power connector. The external jack is only rated up to 3A, whereas the internal one can handle 10A. Section 2.2.4.4 in the TPS. Using an adapter higher than 19V is a safety issue.
Yes, this was going to be my guess. One could set one's mind at ease that this information is correct, with a continuity checker while the NUC is powered off and disassembled. This answer sounds like the external and internal connectors are wired together.
One could then decide to ignore the additional restrictions on the external connector. The 3A rating is surely for any possible application of the connector. For comparison, if one has ever studied wiring power ratings, one can put an amazing amount of current through very thin wires, with proper cooling. Yet if one glances at a typical table, it is conservative but expressly for bundles of 100's of wires packed tightly together with no cooling. A parallel setting would be pasteurizing food. The FDA offers very conservative single numbers as guidance, while the sous vide community understands this to be a complex interaction between time, temperature, and thickness. Does a single number have 10% headroom for a NUC power connector? My guess is of course.