In some sports, American football included, a strategy to secure the win is to employ methods to make sure the time runs out. That's all you need to know to get the point.
Running out the clock

Players, having enough time, who see the draw, or the inevitable checkmate, can chose to run out the clock to avoid checkmate or draw. Is this ethical? Absolutely NOT, but it is legal. When a player chooses to win in this fashion, he wins the game at the expense of his dignity, self respect and honor.
What is unethical/undignified about trying to win on time in blitz? By the way, I see top players on here frequently win this way and I never once thought they were doing anything wrong. As you said, blitz is not chess but "beat the clock." In blitz, if you budget your time better or give your opponent so many problems over the board that he doesn't have time to convert it into a win, I say you've done your job.
Nakamura commonly uses beat the clock.
Think about it: If a player uses more time than you, he has a better chance to get a better position. Why should that be fair?
Well it is, because it's balanced by the clock time, so "beating the clock" is totally fair and ethical, just like it's ethical to use more time than your opponent to make moves.
At the beginning of a chess game, all factors are agreed upon by the players. Then, everything goes by the rules.

I will go for the illusion of the win and for the instant gratification every day of the week :-) !!!!

(by the way - I do hate the player who has K+R+2p against my K+R+2p (all K-side, all symmetric and no play) and 1:39 minutes on the clock, when I have 1:13, and who will play for 79 more moves (moving a pawn in time to avoid the draw of course) just to beat me on the clock)

celot, You said trying to win on time in blitz is unethical, not dignified, and dishonorable. I am curious to know why.

Some of these speed games are actually quite profound, and you'd be surprised at the amount of ideas existing even in a 3 0 game.
If I go together with you over one of the games I lost or won (or drew) in this time control - you'll really be surprised at everything that went there "behind the scenes", or behind the moves - or everything the players saw, when they decided to play this move, instead of that move - and yes, even though they only took a second or three to play it.
These games do end on time sometimes, it is true - but in a majority of cases it's the chess that decides, even in this time limit.
Some long time control games are also decided by the time factor, by the way.

celot, I agree with you. Blitz is its own beast, a large part of which is beat the clock. I'm just surprised when this aspect of the game is not always recognized by some as a legitimate way to win.

<NM Gbidari>
This scenario, K+R+2p vs. K+R+2p (let's say, all on the g- and h- files, no play), with 1:13 mins to you and 1:41 mins to your opponent, with your opponent going Rc2 - then Rd2 - then Ra2 - then Rf2 - then for a change Rc2 again - then ten moves later Rb3 (so no threefold repetition) - and he'll play for several minutes to flag you -
So this scenario, you'll be sitting there and saying to yourself with complete zen serenity - "yes, it's a legitimate way to win" ? :-)
Or you'll be like '!@#$?#%^& this son of a dog bastard'?
In other words, is your position mere rationalization, or do you genuinely feel as you write?

<celot> yes - these factors you cite definitely contribute a lot to an overwhelming feeling of frustration!
You know that you understand chess better than your opponent - and you think - 'they get lucky again... it's this mouse / internet connection'.
Then you find a place where the computer works faster - suddenly everything is smooth, you gain 150 points... life becomes pink and rosy :-)
Well, in football actually there is a rematch afterwards.
Oh no! He is not talking about the old and good football. (Only Joke)
I am a beginner and only play rapid games, but I also noted that if time it's over, the people "prays" to you request a draw, even if you are winning.
In some games, the players like to use engine, because after I run the Stockfish, the engine gave me the same positions... So run out the clock, in the beginner rate, I think it's a good thing .
Nakamura commonly uses beat the clock.
Think about it: If a player uses more time than you, he has a better chance to get a better position. Why should that be fair?
Well it is, because it's balanced by the clock time, so "beating the clock" is totally fair and ethical, just like it's ethical to use more time than your opponent to make moves.
At the beginning of a chess game, all factors are agreed upon by the players. Then, everything goes by the rules.
Time controls were initiated many decades ago; primarily for the sole purpose of limiting the time that an entire game consumes. Some games take many hours to complete. A player faced with an untenable position could, without any time control, sit and stare at the board pointlessly for hours trying to find a way out of an inevitable mate and, to the frustration of the other player. Time control was originally not intended to be reduced to micro-second moves. Such ridiculous micro-mini time allotments bastardize the game of chess. It can be agreed upon to engage in such non-chessense, but it is not chess, its micro-skittles. In such engagements there is NO winner. Both players lose touch with real chess in exchange for the illusion of a win and instant gratification.
Your argument only holds for classical chess / competitive games. No one ever complains about being flagged in time scrambles, given the standard 5 second delay/increment (plus the 2+1 hrs).
Bullet chess was clearly invented to make the clock a major factor in deciding the game.
Your argument might be restated: "Bullet is not 'real chess'," to which I would agree. But it is pretty fun.

solskytz, you've hit upon an interesting point. At the risk of sounding like I am contradicting myself, there are some situations and this is just my personal preference, where I do not try to win on time. If it's just rook vs rook and it's mindless shuffling, I will offer a draw even if he's about to lose on time. In chess there are instances where you can get a TD and claim insufficient losing chances. If I feel my opponent has such a position I will take the draw if offered, as in the situation you described. If my opponent uses such scenerios against me, I can only blame myself for not budgeting my time better.

<NM Gbidary> in this case our sentiments are very similar.
Of course for the benefit of less experienced players, it bears mention that in this scenario we discussed, it's impossible (under FIDE rules) to claim a draw due to insufficient losing chances in an official BLITZ tournament.
And as to your conclusion - I would only add, that I will also take measures to avoid, as much as possible, playing that same player again. I believe that sportsmanship and the general good atmosphere in playing the game, should also count for something.
I basically play chess to have a good time - win or lose. A bad sport spoils the fun.
I don't get any of this: the player who 'runs out the clock' simply loses...