One thing that occurred to me, is that if people aren't playing high level characters because a campaign dies off prematurely (ie, before intended) that is not the same thing as if a character was only intended to be played up to a certain level.
So the question is, are people not playing high level characters because even though they intend to, they start at level 1 and the campaign dies first? Or are people not playing high level characters because they don't want to (or their DM doesn't want to run games for them)?
The first case is more difficult to deal with, but as far as getting more use out of those levels, I'm a strong proponent of playing adventures and campaigns at the level that makes sense, rather than insisting on starting a character at level 1.
Three examples I ran early in 5e:
-A theme adventure (10 sessions I believe) for a party of four 10th-level questing knights in shining armor. (One Devotion Paladin, one Battle Master Fighter, one War Cleric, one Hunter Ranger.)
-A "Savage Kings" theme adventure (about 15 sessions) where the players each played a giant ruler (all the true giant types except stone) in the ancient times when dragons and giants ruled the world. I had to make up some sort of makeshift ECL thing to do it, so the Storm Giant ended up 6 class levels (bard) while the Hill Giant ended up with 15 class levels (barbarian) and I estimated the characters were all about equivalent to 20th level.
-A 20th-level one shot (that took 2 or 3 sessions) where one of the characters was a resurrected PC from our Lost Mine of Phandelver campaign that ended in almost a TPK (survival tip--don't chase the dragon down for a rematch when it knows you're coming and has time to prepare for you), and the rest of them were brand new 20th level characters that the players just wanted to play with.
Playing from 1-20 in a single campaign is a great ideal (and I'm going to do it with my current campaign, even if it takes literally 20 years (and it probably will)), but since it isn't practical for most people in a normal play style, there need to be other options on people's minds.
Here's a really simple method: career snapshots. Let's say you have a campaign you want to play in a year or something and want to get all the way to 20th (or whatever) level. Instead of the crazy forced super-fast XP of 5e, and/or expecting more sessions than you'll actually do, just have the campaign focus on certain parts of the characters's adventuring career, and say that there are months and years in-between those. Skip to the levels that you want to play. So maybe you play four sessions at 1st level, then advance the clock a couple of years and play eight sessions at 5th level, then six at 10th, eight at 15th where you hit the adventure climax, and then two or three at 20th for a brief follow-up to see what happened in the aftermath and play with 20th level toys. Now you've run a 1-20 campaign in less than 30 sessions (and without having to level up after each session). And you could do a lot less sessions and completely different level ranges.
All of this stuff needs to become more common. Starting at 1st level should be a choice, not an expectation.
If people want to play higher levels, but aren't getting to, that's a problem, and that's why I recommend solutions. If people just don't want to play at higher levels, that may be a problem (if the game is making those level less enjoyable) or it may just be a preference for a playstyle that doesn't scale well into higher level.
High level play needs to be different. If playing at high level is the same basic experience as playing at low level, just with bigger numbers and more stuff, then I find it quite likely that you will be bored before you get there. "Another fight against a bunch of goblins led by a goblin boss? Demons led by a balor, whatever, same diff." High level play should involve changes in expectations. Different sorts of challenges that can't be solved by straight up combat. Perhaps political intrigue, leading armies in battle, traveling the multiverse attempting to unravel divination-resistant mysteries, etc. But a 6-8 encounter adventuring day just isn't believable at high level very often (if you are fighting in the Blood War, where it makes perfect sense to run into fights with dozens of high CR opponents that are a challenge even for a 20th level party, that's one of the few times this does work--and perhaps more products supporting setting believable high-level combat challenges like that would be nice). You need to change the play style to something else. Again, if the reason that isn't happening is people few people enjoy those variant play styles, then that's just preference and cool.
I think I had more to say but I lost my train of thought. The point is, I don't think we should just shrug and say, "Oh well, I guess we should just forget about high-level, since no one is using it". There are so many more interesting ways to bring high-level play to our tables and enhance our D&D experiences by thinking outside of the "start at 1st-level, play until you get bored" box.