Losing on Time is Much Worse Than Making Bad Moves

Several years ago I played a series of 20 0 (20 minutes per game with no increment) games against an expert-level opponent. Being the better player, I often found myself in superior positions as time ran lower. For the sake of argument, let's say we often reached a point where my winning chances were 60-70% and we both had 2 minutes remaining.

But then something odd happened.

My opponent, contrary to most experts, refused to speed up to try to avoid losing on time. I, on the other hand, did speed up. What inevitably happened was that we would make several moves and I would still have over a minute left when my opponent lost on time. So I would duly claim the win, but then my opponent would make the unusual request

"Would you like to finish the game?"

Unusual because the game was over! Now during those past few moves my position would often deteriorate slightly as I avoided flagging (and my opponent continued to play slowly). Let's say my "final" position, if the game were not over, would now be completely even.

However, if we look at the "overall" evaluation (properly taking time into consideration), as my position slightly deteriorated my chances of winning (and your willingness to bet on me!) would soar from 60-70% to 100% once my opponent had so little time that he could not checkmate me before his flag fell. 

While my expert opponent's attitude is extremely unusual for players rated 2000+, it is much more common among weaker players, especially those who grew up playing without a clock. For many of them, they would rather let their flag fall, even in equal or superior (!) positions, than hastily make "bad" moves.  While this is, in a weird way, somewhat admirable, it is also quite wrong and often leads to stunting their growth as chess players.

Let's start with the rule book. Basically there are three main ways to lose a game: get checkmated, resign, or lose on time (when the opponent has mating material). All are scored equally: 0.  It does not matter if you get Fool's mated in the opening or last 100 moves, it's scored (and rated) the same. Similarly, if you lose on time,