I am not saying that those are the best shows of the last 52 years; I am saying that they have entered mass consciousness the way very few shows have, and have not been impacted when the original cast left. I can think of only one show that entered mass consciousness, only to fall steeply when the original cast left, The Producers. Maybe DEH will fall into that category, but I don't think so.
Only time will tell. But DEG has a number of things going for it that The Producers did not.
1. With The Producers, Lane and Broderick were big theatre stars when the show opened. They were famous (certainly to the theatre crowd and the tri-state area) and they were all over the place for awhile, basking in the acclaim. When they left, the follow-on casts were not as good as them by a mile: no-one could come close to Lane for his larger than life charisma and they had great chemistry together. Ben Platt was not famous and, beyond Broadway, is not famous now. Plus, if anyone saw him on Will and Grace, they probably concluded that the show was a hit because of the show.
2. As someone pointed out, DEH is going to be on every school must see list for the foreseeable future. High school kids are going to see it, and their younger siblings will want to see it.
3. It has hit a nerve. Whether the show is a little contrived, as some on this board claim, it doesn't seem to matter with audiences. All three times I saw it, many audience members around me were in tears during the last two numbers. That really doesn't happen often. It has an emotional pull that may be stronger for occasional theatre-goers than the frequently jaded participants in this board.
4. The show is going to have a special pull for anyone who felt themselves an outsider in high school.
5. (I am assuming that) the weekly operating nut is modest, and can be managed effectively when grosses start to go down.
Not that this is actually relevant, I will remind everyone of the discussion as to how quickly Hamilton business was going to go down when Lin Manuel Miranda left Hamilton. There were a number of posters who were convinced that the zealotry would die down pretty quickly even if business continued strongly for awhile. From where I sit, it is harder to get tickets to Hamilton a year and a half after Miranda left than it was when he was in it. I was always able to find a few non-premium tickets here and there the first year. Now, I don't seem to have any luck at all (I must admit that I never seem to know when the next block goes on sale, which doesn't help). While I am not comparing DEH to Hamilton, I do see fervor that very few shows achieve.
I am NOT saying that I expect DEH to run anywhere near as long as Hamilton. While I do really believe that DEH could run for a decades, I am assuming that Hamilton will be around for several decades, and that, for a time, the four longest running shows in Broadway history will be, in order, The Lion King, Phantom, Wicked, Hamilton. I don't expect to be alive when that happens so I will not be around to say I was right (or, oops, I was wrong, Chicago is still running). I also realize that, for The Lion King to make it to #1, Phantom will actually have to close at some point.