It's gonna get much worse when you start to try mapping days of the week onto the new times. Are days gonna be the same everywhere as well, to stay from 0 to 24? If so, have fun saying things like "Let's find a time on Wednesday/Thursday". People likely couldn't be bothered and would probably just use the day that their normal wake-up time falls on to mean the full solar day instead. At which point you could also just say okay, weekdays are still following local solar days. But now what weekday is it halfway around the world? Now you need to look up their solar day.

All this to say - abolishing time zones will introduce the reverse problem for every problem that it seemingly solves. You can't change the fact that our planet rotates and people in different locations will follow different schedules. Turning the lookup-table upside down is just a cosmetic change that doesn't remove the situation that's causing the confusion. I'd rather just stick with the set of problems that we're already used to dealing with.