The article you linked seems to be arguing pretty strongly against leap hours. I'm not sure we could solve all those problems even in 3000 years. Can we compromise and use leap minutes? That way the problem is a bit more immediate, in 50 years we're sure to have solved it; or we'll all be dead and it will be on someone else!
Instead of leap hours we could just permanently abandon leap anything, and state that the offset between UTC and TAI is fixed at 27 seconds from now on, forever. Every few thousand years, when this new UTC has drifted enough from solar time on the prime meridian for people to start noticing and caring, countries can decide to simply change their offset from UTC, which will just be a normal update in the time zone database that doesn’t need to be coordinated with anyone else, i.e. something that already happens quite regularly.
This is all quite hypothetical as it’s hard to predict whether anything like our current technological civilization will exist thousands of years from now, but even if it does, a simple mechanism exists to avoid problems (just have each jurisdiction change their local time when they decide they want to).
I can’t see any downsides for literally anyone from this proposal, other than the insignificant downside to the British that they will lose the prestige of being the place that global standard time is based on.
It infuriates me that the BBC World Service insists on announcing the time as "<something> GMT", pronounced in a smug tone of voice. The GMT timescale no longer exists; nobody broadcasts it. What the announcers are broadcasting is the BBC's ignorance. I find it embarrassing and jingoistic.
They've also adopted an idiosyncratic way of pronouncing the time itself: "The time is Four, GMT". Everyone else says "Four O'clock", or "four hundred hours" or "four AM". The Beeb are almost completely immune to complaints; they've outsourced their complaints department, and the contractor's brief is to make sure no complaints reach programme makers.
