There are many psychological factors and attitudes to timekeeping, especially considering (and explaining!) the diversity of means today. Some people like gadgets and don't mind wearing a dedicated timepiece in addition to half a dozen other things in their pockets that would also meet the need. Some want to centralize everything into their mobile phone / pocket computer, but might prefer a wrist computer if one ever became available. Some simply prefer antiques like wrist or pocket watches, or consider these status symbols. Others want to see timepieces on the walls for the same reasons of prestige and custom. The very act of summoning time from a gadget may be too bothersome to many; others may hate cluttering up their view with extraneous information.
But all that's just one aspect of the issue. Would people stuck on a five-year mission inside an (admittedly largish) tin can prefer constant reminders of time, or rather the deliberate hiding of timepieces? I could well see Scotty being ordered to rip out 203 time displays two months into the mission and install soothing chimes or colorful GNDN junctions in their place... Kirk would check the exact time when absolutely forced to, but generally he'd prefer hearing four bells to denote his duty shift start.
There's also the issue of appropriate futurism. On many an occasion, our heroes are able to keep the time to remarkable accuracy somehow, without any visible means - say, when imprisoned without their gadgetry. For Spock or Bashir, this may come naturally. But do the others perhaps have implanted timepieces, right next to their implanted universal translators? This could be a feature of the general population rather than something for Starfleet officers only. The military might still require more robust and reliable means of timekeeping aboard the ships, hence various basically redundant displays.
Timo Saloniemi