I think people who grew up with later ST series often don't know the first one, but people who grew up when all of them (well, nearly all, there's of course still more stuff being made) were available often do. My kids are about as likely to reference ST:TOS as the later series-es.
Similarly, there was a stage of "Paul McCartney was in a band before Wings?" but now the sort of people who are into Paul McCartney (which is not unheard of among people my kids' age, though obviously far less common than it once was) all know about the Beatles. I think you reach a point when all the people who Don't Like Old Stuff fall away and anyone who likes any of this stuff Likes Old Stuff and isn't put off by some of it being from the 1960s.
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Similarly, there was a stage of "Paul McCartney was in a band before Wings?" but now the sort of people who are into Paul McCartney (which is not unheard of among people my kids' age, though obviously far less common than it once was) all know about the Beatles. I think you reach a point when all the people who Don't Like Old Stuff fall away and anyone who likes any of this stuff Likes Old Stuff and isn't put off by some of it being from the 1960s.