Do you think the game could use event announcements?

[Felis]

what do the ps4 users do when they don't have a comp nearby to use the website as effectively as one who would?

going oldschool (pen and paper), or write a macro that list the times ( /echo time; item (slot); location)

I mean if they put a function like FFXIVclock.com ingame, then what would be the reason to hide the times in the gatherer log?

[Meraii]

I mean if they put a function like FFXIVclock.com ingame, then what would be the reason to hide the times in the gatherer log?

Personally, I think it would make sense that once you've found it, the time you found it should be recorded in the log.
With all the addons or whatever it's not really necessary, but from the characters perspective, why would they not write down that they found x node in the morning/midday/evening in z zone.