Would this clock time mode be useful at all? I want to encourage more games to be played with "thinking" chess instead of "video game" chess like in lightning and blitz.  When I play at super fast time controls, I tend to stop calculating at all and just push wood.  So my chess thought process becomes very sloppy, which makes those fast time control games pretty much useless to me in terms of improving my level.

What if there was a clock mode where a minimum time was required to be spent by a player on a move like say 10 seconds and if this rule were violated then the game would be forfeited?

I know that time delay and increment already exist, but I find there is too much temptation to gain time on the clock and move quickly.  

I guess what I want is to find a clock mode that doesn't tempt me to turn off my calculating brain but where the games finish reasonably quickly.

Any thoughts on this idea?
Perhaps this could be somewhat useful in practice games, but I don't see much point in having a minimum time control in real games. Some reasons (let's assume the minimum is 10 seconds but could be any number):


sometimes you are doing forced moves (or known opening moves) where having to wait 10 seconds would be annoying
conversely, there are situations where you have to think a lot longer than 10 seconds, so here the minimum time would not help at all
you might run into the problem that you end up trying to make moves just after 10 seconds (particularly in time trouble), with the added annoyance that you now also have to keep track of when 10 seconds have passed


Overall I think that you should rather try other methods like sitting on your hands, analyzing your games with respect to time spent on moves (and relation to blunders), etc. to improve your time management. An important factor in improving your chess is also to know when to spend more time and when you can make more or less automatic moves.