That said, interestingly, the quadratic nature of that problem (the earth slowing down progressively faster over time) means that the gap between when we have to care about my solution (because we accumulate too many leap seconds per lifetime) and the leap second solution (because you can only insert a little over 365 per year with the current protocol) is much smaller than the gap between now and when we would have to care about my solution.

If you're not too picky, the two solutions "expire" around the same time. The max rate of leap second insertion only admits an hour of drift per decade, which is slow enough that I still think most people wouldn't care, and they might like if our time handling is simple enough that we can't repeat the recent xz supply chain issue in hundreds of thousands of lines of increasingly complex datetime nonsense.

Even if/when humans again walk on the moon it will just be a short trip and they will head back to earth (Likely China, but India is realistic, other countries that could realistically send someone to the moon don't seem very interested in trying) Their missions will be planed from Earth, and they will otherwise want to match earth time so they can contact people back on Earth.

If in the distance future we put colony on the moon, the people will drift apart from earth and so I expect the kids born on the moon will not care about earth time so much and may eventually demand a switch to moon time. OTOH, I think what they really want out of moon time (light cycles are too long to be useful humans) probably isn't what we think today.

Although I guess an equilibrium will necessarily be reached after a sufficient amount of rock-throwing.