Even what you've just described has problems because humans don't think about time in a consistent or logical way that follows real rules that work across different humans in different places. We literally do not think about time in a way that follows rigor or rules, so there cannot be a rigorous computer system which satisfies all the humans involved as it's axiomatically impossible due to being in a world with no axioms! Trying to talk about "time as humans experience it" is like trying to create a definitive list of the "best books of the century"; you can't do it because that's just, like, your opinion man.

If I'm in Portales New Mexico and I drive to see my sibling in Muleshoe Texas at what my clock says is "8:30 AM", that'd take me approximately 40 minutes, allowing me to arrive 9:10AM where I can grab a breakfast sandwich at McDonald's before meeting my sibling for shuffleboard. Except whoops I crossed a timezone discontinuity there, so actually I will arrive at 10:10AM and McDonalds will have decided to stop serving breakfast even though I'm hungry for eggs and the clock in my car happens to read "9:10AM". This isn't some reason to "do away with timezones" because that'd still have the same problem w/r/t travel and different perspectives; if I jet to London from NYC then McDs will also not be serving breakfest when I am hungry for eggs and my (unadjusted since boarding the flight) ticking Timex on my watch reads 9:10am. It's not solvable because people are experiencing different "times" in different places. Either we abolish the concept of time and it's always "whatever number my spiritual essence dictates in this moment via gazing at feeble mechanical devices that I enjoy the aesthetic of" or we swing the other way and all humans record all time in UT1 and we treat the shifting light beyond our windows as a mere inconvenience. We've done the latter with computers because they demand such rigor, implying we'll never do the former and abolish time (it's too useful!), and humans won't all abandon being bound to the sun and its vibes, so here we are in a world where we try to please the fickle and unreliable humans, ourselves, with the cold machinery of our computers (may their flickering lights forever bless us, amen).

Thus, there is only "what's an easy way to represent time that humans won't hate too much?" For most everything, that's "store it in UTC/UT1 and then convert to nearest approximation of what the user wants based factors like 'where are they now?'". Every other approach has pretty big downsides or potential failure modes. For example, if we use the system you just mentioned with a "just time" is "to do anything with it you also have to store enough info to turn it into the other representations". Thus, questions like "how far away is new years eve for my friend across the world?" will be confidently incorrect unless you account for the sun being up here and the sun being down there (typically via the timezone concept). Storing in UT1 at least means you can give the user a time that obeys axioms even if the user has to do a little legwork to adapt their brain to it, which most folks who _depend_ on timekeeping are willing to do to make sure things don't go awry.