Some of us have a real world clock on the wall. They might be old fashioned, but still useful!
Joking aside, that would be a nice feature as a cool detail. It might confuse people if it showed Central time zone, but that would really make Central the official Spiral time zone. If it showed the time local to everyone, wherever they happen to be, there would have to be some way to set those clocks. I'm guessing it is more complex to achieve than it might seem. Maybe not changing the old furniture clocks to make them run, they could make a special crown shop item clock that would run and tell a time, a grand Central Time Clock perhaps, looking like one from an old train station.