Oh I forgot to make 1 last point. Any game less than 6 or maybe 8 minutes should not have the "jerk" button. Worst case you are sitting and waiting for 5 minutes. Im not sure where the line is but blitz games shouldnt have it.
Also filing a complaint on the offender is worth doing. The site admins would have stats to see if the offender was a habitual jerk time out player.
This very scenario happened last night to me in a 15 min game. My opponent was dead lost and just let 13 minutes tick off. I think a possibe solution could be a fuction of the total game time. An example is in a 15 minute game if more than 1/3 of the total game time (5 mins) has ticked by then do a "are you still there" popup with 10 to 20 second response time or actually have the opponent waiting get a choice whether to pose the question or just continue waiting. In a sixty minute game if 10 to 15 minutes have passed then pose the question. I believe both examples give ample time for the opponent to make a reasonable move. More than likely if it takes more time than 1/3 of the total game time the opponent is just being a jerk.