Undoubtedly, the most meaningful definition of "serious aperture" relates to the optical resolution reach of the scope - what is it capable of resolving with articulate sharpness and sufficient brightness, without unacceptable aberrations.
Nonetheless, a meaningful (nonoptical) informal correlation with "serious aperture" used to be the size where it is no longer possible for average-height people to observe near the zenith without aid of a stepladder. That's because it used to be forbiddingly difficult and expensive to obtain consistently high-quality mirrors below about f/4.5. The dividing line fell between 15-inch f/4.5 scopes at the upper end of "don't need a ladder", and 18-inch f/4.5 scopes at the lower end of "need at least a two-step stool", with 16-inch scopes in ambiguous territory, depending on your height. Beyond 18", and you used to need a regular multi-step ladder at least four to five feet high for an f/4.5 20" scope.
Now, however with consistent high-quality sub-f/4.5 mirrors becoming available from a limited, but sufficient (to meet current premium-price demand) number of sources - f/4.2, f/4.0, f/3.7 and even f/3.3 mirrors...this "stepladder" heuristic is becoming badly frayed (at least at the highest premium end of the spectrum), and 20-inch scopes have replaced 15-inch scopes as the upper bound of "stand on the ground". Another informal (nonoptical) heuristic measure these new very fast f-ratio larger-aperture scopes have recently frayed is the distinction between scopes small enough to be easily portable in an average-sized sedan, vs ones requiring a more ample vehicle, which used to correlate roughly (though imperfectly) with the "stepladder" heuristic. (Maybe it still does, though shifted along with the stepladder heuristic toward 20" instead of 12" or 15").
One informal optical measure is how overtly the aperture is capable of showing spiral structure in how many galaxies under say, mag 6.0 skies. This can start with as little as 10" or especially 12", but occurs much more readily with 18" or 20". I've heard lots of people comment that good 20" scopes is where significantly more detail begins coming out, just as 10"-12" seems to be another similar lower-level quantum boundary.
This is like the rest of your posts, astute, well-reasoned, and based on considerable experience. Excellent.