If we abolished time zones, it wouldn't make sense /ever/ for people in some parts of the world, even when communicating with people close to them. That's worse.

That's already the case for people very far North/South. Summer/winter become their own day/night at the poles... according to the Sun. If you take a walk around the pole, you can cross several timezones and end back where you started while having "lost an hour" every few steps. Of course, in one of those crossings you "gain a day" so, watch your step!

Why wouldn't it make sense "ever" in any part of the world?

In some areas, standard workdays would span "days". So e.g. a business would need to post its hours as "M-F, 00:00 - 1:00, 17:00 - 24:00". (actually it's even worse as the last 00:00 - 1:00 is on a Saturday)

Or imagine chatting with a friend at 23:00 about plans after you get off work at 1:00 the following "day". "See you tomorrow?"

Or do you reserve "tomorrow" for telling someone at 8:00 that you'll get back to them when you wake up at 16:00 that same "day"?

Today people only have to deal with this when communicating with people many time zones away, but now it's an issue even within a single area!

Which defeats one of the supposed “benefits”: “meeting at 2PM” means the same everywhere.

"Meeting at X" means exactly what it always meant. The only difference made by removing timezones is that you don't need to adjust the time for remote dial-ins. 2PM becomes 2PM everywhere.