Well, the sequels are in production. Their success (or lack thereof) will be a big indicator of the premise’s staying power.
As a thought experiment, I reviewed a list of Oscar winners and nominees for Best Picture going back to 1960 (arbitrary benchmark), to see if there were any cases where one of the nominees had more cultural staying power than the winner. I’m not trying to assess if I think the nominated film was better than the winner, just if it would be more broadly familiar to a modern audience:
1963: Winner: Tom Jones. Culturally outshone by Cleopatra, though I think largely because of the tabloidish antics of its stars.
1967: Winner: In the Heat of the Night. Culturally rivalled by Bonnie and Clyde and The Graduate.
1970: Winner: Patton. Culturally outshone by MASH*, though I’m sure entirely on the strength of the TV series.
1977: Winner: Annie Hall. Culturally outshone by Star Wars.
1980: Winner: Ordinary People. Culturally outshone by Raging Bull.
1981: Winner: Chariots of Fire. Outshone by Raiders of the Lost Ark.
1982: Winner: Gandhi. Outshone at the time by E.T. the Extra-Terrestrial, but I propose E.T. as being a classic example of a film with a massive following in its day but which largely culturally disappeared afterward.
1992: Winner: Unforgiven. Edged, I think, by A Few Good Men, though mostly on the performance of Jack Nicholson. At the very least, “You can’t handle the truth!” is still familiar, but I can’t think of a single quote from Unforgiven.
1994: Winner: Forrest Gump. Rivalled by Pulp Fiction, possibly by The Shawshank Redemption.
1996: Winner: The English Patient. Outshone by Fargo. Jerry Maguire made quite the splash in its day, but aside from “Show me the money!”, I don’t think it had much cultural staying power.
1998: Winner: Shakespeare in Love. Outshone by Saving Private Ryan, not least for the idea that SPR has become a defacto standard by which the realism of epic war movies is often compared.
I’ll stop there, since the movies are getting too recent to judge cultural staying power. I figure 15 years is minimum.