Currently when you state a time you are almost always implying your local timezone applies, which might be unknown information to the recipient, especially with written sources like these comments here.

In most people's everyday life that's really rare. And when it does happen it's usually clarified. In more automated contexts (e.g. a scheduled YouTube premiere) the software converts it automatically - the author inputs the date and time in their own timezone, and viewer sees the converted date and time in their own timezone.

When it does happen it reminds us that the date and time falls on a different time of day for different participants.

With everybody using the same timezone instead you would always make an unambiguous statement about the specific time by default.

22:00, midday.

Person A: "Meet me here tomorrow at 01:00"

Person B: "Sure no problem"

... three hours later ...

Person A: "Ugh, I told him to be here at 01:00, where is he?"

... 24 hours later ...

Person B: "Ugh, he told me to come here at 01:00, where is he?"