I'm ambivalent about day clocks, unless they're too short. Stardew's day is about twenty minutes, so is Minecraft's, and about on par with old Harvest Moon games. When I played My Time at Portia, though, I had to go straight for the setting that doubles the length of the day. Now there's a game with time pressure.
Calendars, though, I think are very important to a certain style of game. With Stardew, it reinforces the feeling of rhythm, ritual, and repetition that is what makes the game so cozy to begin with. A farming game needs a calendar. A cozy village life sim needs a calendar. Even The Sims is better with seasons.