That already exists. It is my daily life in fact. eg "Is 8am PST too early for folks in IST?" literally is all day every day.
For example I literally have 3 emails in my inbox at the moment that arrived overnight from people in California saying some variation on "I saw a slot in your calendar for xpm PST, is that too late for you in London?".
The set of people who care about anything that using one time zone for everyone would fix (mainly programmers who have to deal with time zone conversions) is much smaller than the set of people who care about the things it would break: anyone who wants to understand the shared global culture around local times (for example: anyone who travels to other time zones regularly, or even anyone who watches foreign movies or TV and wants to understand what the characters are talking about when they mention time of day).
That's why I support getting rid of leap seconds, but not getting rid of time zones: the number of people who leap seconds helps is very small (possibly zero) since their effect on everyday life is microscopic.
Yeah I know. I'm not actually seriously entertaining the hope that 2 or 3 happen. Eliminating DST would be I think also be a genuine benefit to almost everyone with very little downside.
People are going to keep living their lives approximately according to local solar time, which means that the meaning of X time in practical terms ("is this a good time to call?") is going to be different from place to place, so people would need some way of looking up the normal schedule of a particular location. And now we've re-invented time zones but probably with slightly different details, meaning that we can't just re-use the old time zone tracking infrastructure as is.