A very useful property of the current system is that calendar days are aligned with solar days and the change of calender date consequently happens when most of the population is either asleep or otherwise not too fussed about the exact date.

UTC-only (or equivalent "global time" proposals) breaks that for everybody not living near wherever the meridian ends up, which causes a lot of weirdness when a single calendar date can suddenly refer to two completely different solar days and two completely different wake cycles.

Additionally, such a proposal would also break all clock time references in fiction, especially when reading works set abroad or in some unspecified (but still Earth-like) setting, but I guess if you don't care about the calendar date weirdness, you wouldn't care about that, either…