The first part matches my experience: I ran an AD&D campaign for 10 years (spanning 1e/2e), it got to 14th level, and that was running weekly, for 8 hours. The second part, not so much - one-offs just run arbitrarily at high level were generally pretty awful, and campaigns that survived to high level got so heavily-modified they were no longer a valid test case.
I never saw a campaign collapse under the weight of the mechanics of the game before 2000
I have, just not necessarily at high level, and not always D&D.

But, again, prior to 3.0, variants were widely acceptable, so if the game did run into issues, you just changed it - a lot. With 3.x/PF/d20 came RAW-obsession, and suddenly you were stuck with the rules, even as they started to fall apart. In lieu of old-school variants re-writing the rules piecemeal, you had 'core only' and E6 games to cope with the problems.
All that nay-saying aside, the two 3.5 campaigns I played in for it's full run did hold together - just barely - through 13th level, and I'm running a 4e campaign that's at 17th, and playing in one that's on the cusp of Epic, as well as running & playing in Paragon and Epic one-offs and mini-campaigns.
I think a lot of people are basing their expectations on how high level 5th edition will play on prior editions
It's the logical thing to do. High level play was potentially problematic in the editions that 5e more closely resembles, especially in terms of 'feel' - if you feel like you're playing 2e or 3e, you expect the campaigns to go like your 2e or 3e campaigns did. They won't though. For one thing, high-level exp progression accelerates instead of slowing to a crawl. For another, there's Bounded Accuracy keeping everyone on the same page like the treadmill effect did. And, most importantly, the DM has a lot of latitude to keep 'em from going that way.
From my reading of the game, 20th level 5th edition looks just as, if not easier, to run and play than the same or equivalent level in AD&D or BECMI.
From just reading it, I'd agree, and it's not encouraging. From actually running it at lower levels, though, I'm more optimistic.
I agree, and I am genuinely excited to have my players get their characters to 20th level and then keep playing, because that once again looks like it is not only possible, but also not labor-intensive, and actually fun.
In a way it's back to the saving grace of old-school, only you don't need to write out reams of variants and educate your players in your customized version of the system, you just Rule in favor of the campaign staying fun in the moment, Rules notwithstanding.
But, the game does top out at 20, so I'm not sure what you mean by that italic bit.