Also not to forget that currently midnight and the associated change of the calendar date happen at a time when most people are either asleep or otherwise don't really care about that fact.
Not having time zones means that everybody except the privileged minority living near wherever the new meridian ends up will have the calendar date change during their waking hours, which will be rather confusing.
Plus how are things that are currently specified at the granularity of calendar dates supposed to work? Do public holidays and suchlike suddenly start and end at something like for example 3 o'clock (solar time) in the afternoon, because that's when the new midnight (global time) happens at your location? Or does everything now need to specify starting and ending hours, too? Or do you decouple the change of calendar date from midnight (global time), which basically means reintroducing time zones through the back door…