The reason to have a visible time for the full game is that it's harder to keep track of how much time you've taken over dozens and dozens of actions vs the time taken over a single action. Adding such a timer for individual moves would not difficult at all, but why do you need one? 5 minutes is a long time, 10 minutes is longer. Try to count to 300 or 600 without getting bored before 200 -- that's what your opponent is doing in the meantime. There's no reason to take every second of your move timer regardless of how much time is on it.
If you really feel slighted by the timer, there's also the Glacial time option with a whopping 4320/1440 minutes (3 days / 1 day) on the clock. Effectively no way to run out of clock on that setting.