In the vast majority of cases, the most salient property of a timestamp, for humans, is what point it occurred in the 24-hour day/night cycle (and, secondarily, where it occurred in the 7-day week cycle).
Local time is an approximation of exactly that 24-hour cycle; the local time anywhere is approximately the elapsed time since the last solar midnight in that location. (Yes, it's not perfect, because in some places local time has a persistent offset from solar time, or even one that changes twice a year, but it's close enough).
UTC is an approximation of the elapsed time since the last solar midnight in England. Most people don't live in England, so this just isn't relevant most of the time.
If we all used UTC, sure, people living in one place would get used to the new correspondence to solar time; someone who spends all their time in Arizona would quickly get used to the fact that they now eat dinner at 12:00 UTC instead of 7pm. But it would make traveling more tedious: you'd have to re-learn the mapping every new place you went. It'd also make communicating with people abroad more difficult. If someone tells you "I went to bed at 08:00 last night", you have to know that in New Zealand that means they're an early riser or were sick; in New York it means they had a wild party and in Poland it means they worked the night shift.
There are a few cases where having a shared absolute time reference is useful; for example, scheduling meetings with people in many different countries, but in those cases people tend to spontaneously settle on a time standard and it doesn't cause many problems in practice. And even in many of those cases, the local solar time is still relevant (you wouldn't want to schedule a meeting for someone around their solar midnight), so you have to have some way of expressing it anyway.