The tube itself has an unlimited shelf life unless there's a defective seal. Even things like flyback transformers wouldn't be impossible to replicate in the future.
They of course don't have an unlimited *service* life, given the inevitable degradation of parts like the electron guns, heaters, and phosphor burn-in, but sure, treated gently I think it's very possible we'll have working CRTs well into the 22nd Century. And given the fact that monochrome CRTs can be built with essentially 19th century technology it might not be beyond the realm of possibility that if someone really wanted to they could set up shop to blow some new ones someday. There's a bit more there than setting up a blacksmith shop, but not many orders of magnitude so.
Like the the EL display in machines like the GRiD compass, data general One (EL model). Dynamac EL, Informer 213. Etc.
These are very reliable. They suffer from burn in like CRT's but I've never seen one fail apart from cracked glass causing the vacuum to leak out (like CRT)
There are still companies making these displays, specifically for ruggedized industrial applications. A major advantage they have over LCDs is they're hardly affected by heat or cold; this is a serious consideration for things like shipboard and avionics displays. Last thing you want to find out after landing your LC-130 at McMurdo Station is that none of your flight computer displays work anymore after leaving the plane shut off for an hour.
Whether the ones back from the 80's that were made cheap enough to be sold in (still very expensive) laptops can meet those levels of reliability is probably an open question. They're so rare I don't know if I've ever seen one in the flesh.
Plasma displays seem to be fairly reliable with no shelf life problems yet, but they were only popular in PCs for a short time, so spares are not plentiful. They also rely on custom ICs that will be impossible to replace.
Maybe they last okay on a shelf, but it seems like it's not at all uncommon for plasma screens in computers to have problems? Seems like it's actually kind of rare to see a Compaq Portable III or PS/2 Model P70 that doesn't have some kind of damage.
Early LCD displays have been very reliable for me as well, (I'm talking about the old green lcd's like in the Toshiba T1100)
LCDs are *very* sensitive to being stored incorrectly. If you find an old laptop that's spent twenty years in a non-climate-controlled warehouse or something there's a really good chance the screen is going to be damaged somehow. Manufacturing techniques for big LCDs were also still in their infancy in the 1980's, so there is a lot of hit-and-miss when it comes to issues like air penetration, contamination, etc. Ultimately I think the biggest weakness for LCDs going forward is going to be the plastic components. You have polymer-based polarizing sheets and glues which just aren't going to be as stable as the glass envelope of a CRT, and most LCD displays also use plastic-based ribbon cables that are prone to embrittlement and (in the case of laptops) failure from repeated flexing.
FWIW, it's not at all unusual for old expensive CRT terminals which had protective glass layers laminated to the front of their CRTs (both for implosion and radiation protection) to suffer from "screen rot" as the glue between those two layers goes to heck, so issues with unstable materials are definitely not
just an LCD issue.