That's a good point. When I used to wear an old Casio digital watch, I would often take it off my wrist if I was going to do any serious timing with the stopwatch.
Of course if you're going to take it off your wrist for any serious viewing, they could have just put a bigger LCD on the tuner device itself, since you have to carry that anyway.
But that wouldn't have the "wow" factor of a TV watch!
When I used to wear a digital chronometer/clock (ahem!) I totally took it off for serious timing. And it was all so serious, when you were the holder of a timer that counted milliseconds.