>For example being 2:00 pm on USA

Where in USA? It has six timezones.

The answer to your question is another question:

How many people will agree for their solar midday (i.e. sun at the highest in the sky) to be at, say 5pm. Timezones are there for people's convenience. Having to account for time zones is something relatively few people have to consciously do, even today. And if they have to, they will usually use UTC as a reference, because it's the reference standard timezones are arranged around.

Even certain countries adhering to am/pm itself just shows what the obstacle would be. You can't have a 4 post meridiem (AFTER MIDDAY) if midday is several hours away. And trying to get them to simply use a 24h clock is an uphill battle, much less accept a time that doesn't align witg their day.

TL;DR It'll be possible to unify the world's time when you, the OP, will happily agree that your sunrise is at 17:00, your midday is at 23:00 and your midnight is at 11:00. Why those times? Because someone else that isn't you decided that their time aligns with solar time, deal with it.