I think when people think of Star Trek they immediately associate it with Spock, but that's alright and says nothing that denigrates any other iteration. Maybe people of a certain age think of Picard/Data. I don't think the latest wave of Star Trek (what do we call it? I can't stand the monicker 'Nu-trek' as it is too often used in the pejorative) has crossed into wider culture in a significant way yet sadly. Maybe a more show with a potentially more accessible format like Strange New Worlds will do that.
However, taking your "We", we all came to the show at different times. I've been a fan since the early 2000s, some people go back to the 1960s, some people got into it in the past few years through old shows on Netflix or through Discovery. The fact is that for a science fiction fan, Star Trek itself is "out there and hard to avoid". If a person likes science fiction, then at some point they will at least cross paths with Star Trek and I believe that will be true in 20 years because it's survived for so long already in one form or another and, whether folks like it or not, Discovery is now part of that.
My point is still that people will be talking about Discovery in 20 years, because it's part of a much larger monolithic entity. To imagine that people be putting Trek 1966-2005 on a pedestal in 20 years while dismissing Discovery etc. as disposable junk-television is what I took issue with (and I'm aware that it's not you that said that). In 20 years time I'm certain people will come to Star Trek as they do now, through old shows and new and through various means.