There are moves to abolish DST and I suspect that after that happens timezones will ossify, which will make it difficult to use them to compensate for a large DUT1. And after 1000 years of gradually shifting daylight, people will probably be used to noon being a bit late and may well prefer it.
In a thousand years it is quiet possible there will be sizable enough population off of earth that trying to align time with the variable rotation of the earth will be seen as pointless Terracentrism
