The public forgot the TNG movies in a matter of months and they appear to remember only two of the TOS movies, so guessing 10 years out is difficult. We, of course, will remember everything.
Whenever a new Trek movie comes along, TV stations (in the UK at least) marathon through most or all of the prior films in the weeks before. They still get seen so long as more are made.
Shhh! I think they have cracked the secret timelord code! everyone understands who you are talking about!
Not to mention that all of the first eleven ST movies are on DVD and still available. Many other movies fall "out of print".