@Static Shadow, I agree with you. No point trying to waste time moving kings around when I have a 10 second increment.
In lightning games (1-2m), it is perfectly acceptable to attempt to time your opponent in any way you wish. Time needs to be weighted against move quality.
In fast blitz games (3-5m + 0-1 inc), it is fine to attempt to time your opponent out if he has little remaining time. Otherwise, attempts are generally fruitless and result in an opposing win.
In blitz games (6-14m), it isn't worthwhile to attempt it. Unless your opponent is seriously down on time (1-2 minutes) with a very low increment, any random move attempts destroys your own position. Use the 10 minutes you have to think and outplay your opponent, who is in severe time trouble. He has 5 or so seconds to respond to your random moves.
What you should be doing in rapid/standard games is trying to use your time advantage to create complex positions, causing your opponent to use up more time and/or blunder/lose game. Not making random moves, leading into a mate in 1 for your opponent.
Generally acceptable: 0+1,1+0, 1+1, 2+0, 2+1
Depends: 3+0, 3+2, 5+0, 5+2
Generally not acceptable: 5+5, 10+0,10+5, 15+0
NOT acceptable: 15+
It isn't the end of the world if your opponent randomly moves kings. After all, it's their choice. It won't waste much of your time (unlike stalling purposely) It's just bad sportsmanship for longer time controls.