Currently you have to know all your timezones and do the conversions in your head if you travel a lot for example. Additionally the organizers of many events and conferences, even very international ones, do not use UTC. So no, UTC doesn't solve that problem in practical terms. If the entire world used UTC for their local time, then it would be a similar solution. I personally wouldn't mind that actually. It would take a bit to get used to but in the long run it makes much more sense in an ever more globalized world.
Same as the world adopting the metric system, and in science specifically SI-units. Surely you agree even though that was a bit of a hassle when countries changed over from their old unique units at the time, in the long run it was the right decision. Imagine what it would be like working in an international team always having to convert units of measurement. It's still an issue in engineering sometimes, because outside of science the US didn't make the switch and it's extremely annoying.
You have to know how the sun behaves at your local position relative to the universal time regardless of whether we call that knowledge "time zones" or something else. It sounds like what you want is for everyone to be more explicit about their time zone: instead of saying "the conference starts at 3 PM" they should say, "the conference starts at 3 PM UTC-6", right? From that you can easily derive that it's 9 PM UTC, and interpret that however you like for your current location.
Maybe you haven't experienced it yet but it's not as simple. I live in different countries and regularly have to deal with this. There's often confusion about time zones. Sure, it's "just a simple" conversion in theory but firstly the point is that ideally you should not have to do this at all and secondly no one calls it "UTC-6". You're lucky if they add a time zone at all, and when they do it's usually "EST", "Beijing time", "Eastern" (which can be Australian, American or whatever, your job to know from context), etc. Then you have to deal with DST, but only in some countries during some parts of the year. And don't forget the countries that add half hours, or Nepal which is extra special with an additional 3/4 because why not. It's utter madness.
Unless you're a savant who can remember all regions with corresponding time zones and all the exceptions, you'd be looking this up, which is what people normally do.
Same as the world adopting the metric system, and in science specifically SI-units. Surely you agree even though that was a bit of a hassle when countries changed over from their old unique units at the time, in the long run it was the right decision. Imagine what it would be like working in an international team always having to convert units of measurement. It's still an issue in engineering sometimes, because outside of science the US didn't make the switch and it's extremely annoying.