If white had 20 min left on the clock and black 0, then white WOULD have won had the player spent the time thinking. Given that white was at least equal or at the most slightly behind, more time spent would have meant a better game, see?
So the issue boils down to those games where the "winning" side loses on time, which is common in blitz games but not so much in 10+ per side games.
That is where fischer time helps (increments added after each move). If you know your opening and the opponent does not, 10 min + 10 sec per move game the stonger player could have 12 min to 8 out of the opening. In a won game, with 1 second left, the winning side can jump 10, 20, ... 2-3 min added to the clock by moving quickly without mistakes, for example shuffle a queen in a queen & king vs king ending, rather than lose on time, the winning side shuffles to gain time and pulls out the win.
Anyway, messing with it is a bad idea IMHO. The time controls are agreed ahead of time, and are part of the game. If you need more time, do not play the faster time control choices? Think of your favorite sport, its march so say basketball. Team A hits a 3 point at the buzzer to come from behind to win after team B has lead the score for the entire second half. Fair? Is team A the better team? No, thats just how time controls work in sports (and chess is loosly considered a sport). Sudden death is a factor and losing to it is a loss same as any other. The players know that going in and expect that time management is part of their game.
The big reason not to do this is complexity. Complex rules that accomplish little are not a good things. I mean, take a typical game between players 250 points apart or so. The stronger player might lose a whopping 15 points or so. With your suggestion, say that becomes 10 points instead. So you added complexity to the ratings -- messing with a decades old system to boot, causing *all* serious players to need a new rating as it totally invalidates the existing rating -- for the sake of 5 points out of a theoretical 3000. 5 points out of 3000, let me say that again. That is 0.16% effect. Its ... nothing?
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