Perhaps the issue isn't the trouble with defining RPGs; perhaps the issue is trying to use definitions to exclude things that you don't like?
I don't think that much would be excluded, entirely, just that it would become easier to evaluate TTRPGs, objectively, with a tighter, more consistent definition. The unofficial/unarticulated definition of TTRPGs is so broad, that exisiting RPGs can be sorted into mutually-exclusive sub-categories, like the unsubtle "ROLE Playing" vs "ROLL Playing" or, obviously, the more intellectualized GNS.
Armed with such esoteric jargon, and misuse of informal fallacies & the like, one can readily paint a good game as bad (in one or two GNS categories) or a bad game as good (in one category) or, simply, if reason ever makes some unwanted inroads in the face of confirmation bias, dismiss all attempts at understanding a game, and assert it's all subjective. (the nice part, no one ever lose an argument, the bad part, no understanding is ever reached)
I suspect a tighter definition of TTRPG would only risk excluding early D&D, it's closest imitators, and freestyle RP. Of course, freestyle RP is still roleplaying and 100% legitimate, it's just, y'know, not a game, let alone a TT game. And D&D, at worst, could be seen as a small scale wargame that crossed a line into TTRPG at some point in it's long & storied history (quite possibly, after my favorite edition, 1e AD&D, and as early as my least-favorite late 2e

). :

: (I mean, that alone, speaks to the subjectivity of taste, lol)
It would mean accepting that some games we like aren't actually that good (which, is freeing, if you give yourself a chance for self-reflection as to why you like it) and some that we loathe are actually OK games (which can be more disquieting to reflect upon).
So, yeah, unpopular opinion, indeed.
