I remember when I thought the same thing. Then I spent a couple hours thinking about it, and realized what a terrible idea it was.
In my day to day life, I often need to talk to fellow tech people (engineers, support, etc.) in my own time zone, but also in places such as Sydney (2 hours behind me) or California (20 hours behind me). As a society, we've agreed that tech people like that are generally working 9-5, give or take, and we have a universally agreed mapping of locations to adjustments to local time (aka, time zones).
This means that I can look at a clock and realize "oh, it's only 10am, I shouldn't expect a reply to my email to that guy in Sydney yet". Even if I'm dealing with a place I'm not really familiar with, I can look up the timezone, or just google "time in Berlin", and I now can translate appropriately.
But what if we abolished that mapping (aka, timezones)? Presumably every location would just continue on about their life as before. Sydneysiders with desk jobs would stop working 9-5 AEST, and would start working 19-3 UTC; New Yorkers in similar roles would be working 4-12 UTC. Sounds odd, but it would quickly start to seem normal.
Problem: We just abolished the mapping tables that let me adjust for local time. It was trivial to work out that my Sydney colleague was probably out to lunch at 12:45 AEST, but how am I meant to know if he'll be out to lunch at at 22:45 UTC?
The only way to make this work is to have or create some form of mapping that tells me the adjustments to make to bring Sydney schedules in line with my own schedule. Eg, "I go to lunch at 00:30 UTC, and Sydney is about 2 hours behind me, so they'll be at lunch now". Because without that table, I simply have no clue what (or rather when) people in Sydney are doing.
But that table is just another word for time zones, the thing we abolished. Even better: While there are work arounds, most of them are very difficult to computerize. For example, I could check the corporate website of the guy I'm trying to call, and see if they have office hours (in UTC), and then try an work out when they'll be at lunch, but my calendar app wouldn't be able to do that. It needs a formal, agreed upon table of adjustments. Which would be time zones, whatever we want to call them.
TL;DR: This is an idea that makes a lot of sense to people who only have to deal with people who are geographically close to them. If you're actually dealing with people around the world, time zones are not an inconvenience, they're critical.