> local time, that would be on
> your phone,
If I have it with me while playing, which I frequently don't, and would even less often actually look at it.

> your computer (desktop),
not in the same room

> your alarm clock,
not in the same room

> your watch,
ok, yes, this one's available

> the microwave in the kitchen,
not in the same room

> the cable box next to your TV,
don't have one (Netflix is so much cheaper and lets me watch shows whenever I want)

> and like 20 other places in most homes.
not in mine

So, of all of those, my watch is the only one available, but I don't play while watching my watch. I play while watching the TV (PS4), so that would be a much more convenient place to show the local time than having to keep checking my watch repeatedly.

Also, displaying the PS4's local time means it will be in sync with the timestamps in the chat log, which wouldn't be the case with any external clock unless both their times had just been set. When there's a timestamped message saying "Pull in 5 minutes" or something, I'd like to know when it's five minutes later.

Sure, this is just a minor little convenience feature, but since the game can already show either clock, having it show both shouldn't be all that difficult to add. Even minor little convenience features can be worth small changes like that.