i think i stopped wearing / owning a watch after 9/11 in the US, about the same time i had an awakening experience.
i suppose it depends on ones' belief
and for me,
time is a human construct that enables us to structure our lives.
Not a bad thing, just a thing. Your last line reminded me of an old poem of mine A Mind Off-Grid, Nr.01 - The Cycle Of The Thing
For a while I thought it was a bad thing
but giving it some time to breathe and tell its story
I subsequently saw it was a good thing
and then further allowing it to play out long and free
I eventually experienced it as just a thing.
Indulging it with yet more time
I observed the thing in other people
and finally far away on the distant horizon --
as I sub-consciously waved it a mental ‘bye-bye’
the next bad thing was slowly creeping up on me. Regarding wearing a watch, I always do and feel odd if I don't. I have two watches, one for work which gets bashed about and scratched, and one 'good' one; it tells the date too -- bifunctional