This is a section for learners including those just starting out with theory. It should not be made complicated with philosophies and what-ifs. The naming of intervals is within a specific system which is based specifically on the standard Western 7-note major scale we all learn. I tried to set this out as clearly as possible in the other thread.
It is an antiquated and therefore awkward system, but it is the system that is used, so we have common terms and concepts within that system. It's the "common" system that is used, and it's set up the way it's set up. It is for written notation. The by-ear player doesn't have to care whether he just played G# or Ab.
The names we get from that system are artificial, but related to real things: the quality of sound of an interval, and a distance between notes measured in semitones. The latter are real. Whether we play C D# or C Eb, the shared sound and piano keys are what are real and count.
There are attempts aplenty to substitute a different system, because it is so awkward. Nonetheless this system is used almost universally, so it's good to have some understanding of the system as it's set up. We should not make it more complicated and scary. Those kinds of speculations might be interesting for some in another section, but not the learner group.