That's what Unix time is... kind of. It's what's usually referred to as an "instant", which is a moment in time that's independent of any timezone or calendar. It's just a plain number that increments by 1 every second.

A lot of systems already store dates and times as Unix timestamps, which means they're already timezone-independent and the timezone and formatting are only applied when rendering it.

In some cases, you do actually need to know the timezone. Calendar events are a good example - an event may end in a different timezone than it starts in (like if the event involves travelling), so both timestamps need their own timezone.

There's also cases where there's no 1:1 mapping between a date/time and a Unix time. Daylight saving is the best example. When the clock moves forward from 2am to 3am, the times between 2am and 3am don't have a Unix time, because they don't actually exist. Conversely, when the clock moves from 2am back to 1am, the times between 1am and 2am have two Unix times - one before the change and one after the change.

That's not to mention outliers like Antarctica where each research base chooses its own timezone.

Dates and times are very complicated :)