You would still need to remember to not call your buddy in LA at your "8am" when in NYC. Now you need to take into account what a 9-to-5 translates to for all parts of the world. Solves nothing.
It actually solves a lot, and I contact people on all continents multiple times per day. Currently when you want to schedule a meeting with a person in another timezone you need to do a bit of very confusing math (it's simple addition and subtraction, but one-off errors are rampant) and translate their time to yours. Most of the time both parties try to do it and it gets confusing. Lots of "your time or my time" questions. With universal time you both work with the same clock.
You're right. Let's completely change how humanity has done it for centuries so you and your friends don't spend 32sec looking up "current time in X" 2 or 3 times a day.
You would still need to do the effort of understanding what 10pm means for the other party. 10pm may be your lunchtime while it's the middle of the night for them.
Don't think people have been having calls across continents for centuries. Just 100 years ago the vast majority of the population would never have encountered another time zone.
You still have to know a bit about your buddy, though. You can probably assume he'll be awake at his midday, but what about 7:00? Is he an early riser? Or does he have other commitments at that time? In reality you'll just learn you can call around 16:00 your time. At that point it's just a number and doesn't matter what it is.
If things really were more complicated and you always needed to ask the question of "when can I call today", would it really be that difficult to incorporate schedules into contact records so your phone can tell you "available after 23 today".
Sort of, but not really. I know what time is convenient to call my parents and they live in the same time zone as me. I don't work it out every time based on what the "normal" schedule is. And that's not to mention who actually calls people randomly over text now anyway?