I guess it all depends on how important your Blitz rating is to you.
Winning drawn endgames on time in blitz

you spent more time to reach a drawn position, if you can't hold a "drawn" position with the amount of time you have left its pretty much your fault.
it would be pretty unethical NOT to let your opponent play on if they have way more time than you.
in a real tournament it would still count as a loss towards you because the position isn't drawn enough.

I don't hold it against people for playing on time in blitz because time is such an important aspect of the game, but i do try and offer draws in COMPLETELY dead positions, as in you can absolutely only shuffle pieces, like rook v. rook or opposite colored bishop fortresses. a rook endgame with pawns on the board, even though it's obviously a draw, i wouldn't feel bad for playing on as long as i was still moving pawns and at least trying to maybe set a trap for my opponent.

It is more sportmanlike to accept the draw. And the higher your rating differenc, the more sportmanlike it is. I know a 2300 who was winning by 3 seconds ( I had 3 seconds left) and in a completely drawn position, kindly accepted my draw offer.

If the game had been one minute shorter you would have already lost on time. You knew what the deal was when you started the game (or if you didn't, you do now). Personally, I don't play out meaningless games where I have nothing to learn because my time is more valuable than that, but if other people want to, that's their prerogative.
Why not save your time & resign? Because it would affect your rating, right? Well, I guess that's the very reason your opponent kept on playing to try to win on time, so by not quitting you are really only playing for the same reason.

I would be hard pressed to say winning that way is unethical. What rules have been violated? Who has been taken unfair advantage of? I might agree that it is a petty way to win, but it is part of blitz. As other posters have said, if a person doesn't like losing this way, they shouldn't play no-time-increment blitz.

in a real tournament it would still count as a loss towards you because the position isn't drawn enough.
Questionable. I don't see that White made any progress during the last 50 moves. So a 10.2. claim should suffice to net the draw.

Why not save your time & resign? Because it would affect your rating, right?
No, because it is a dead drawn position. According to your logic I would have to resign against a GM on move 1 because I will lose anyway.
two sugestions,
I made a thread about 3|2 being a much better time control then 5|0 and part of it is this reason. Play 3|2, its almost as long as five minute but the board plays more factor. Its much better for when you are winning also.
My other tip is if you know for sure you will lose on time get them in the rapid moving mindset and then try a sneak attack with the rook. I have won a couple of games with this cheap shot.
Really the worst position is a drawn opposite colored bishops with less time.

in a real tournament it would still count as a loss towards you because the position isn't drawn enough.
Questionable. I don't see that White made any progress during the last 50 moves. So a 10.2. claim should suffice to net the draw.
The insufficient losing chances rule doesn't work in blitz. It needs to be a game in a standard time control, without any delay or increment. In blitz, managing your clock time is important regardless of the position on the board.
When I reach similar positions where I am up on time but it is a dead draw, I always offer them a draw to be nice, but most people don't do that, and It's completely fine.
Shuffling is within the rules, but plain silly/idiotic. The main obection to sudden death time control is that you are given a limited amount of time for practically unlimited number of moves. for example, a game could end on 20 moves or 200 moves [50 moves plus 150 mindless shuffling]. one can never manage tome reasonably well with such strange rules provided for a game where silliness is more important than chess skill. This is why it is vitally important to have an incremental time control (+1s would be fine) so that reason and skill becomes a larger factor than idiosyncrasy.
sudden death time control is never a serious game format, and they are not to be taken seriously. in chess, time allotted should always be the thinking time, and that should not include the time taken for actually physically moving the pieces.

I think he means "while there's enough material to achieve checkmate". Otherwise it would be draw before time runs out.

Yeah, that was completely drawn and stupid to play on, but as many predecessors said, it's ((un)fortunately) a part of blitz.
Don't worry, we have the same people in Slovenia. I was playing a blitz, the situation was almost the same except we had one bishop each. I was also down on time, with 15 seconds left, my opponent had 40. We shuffled the pieces and suddenly the repetition occured. I claimed a draw and declared game over. BUT there was no arbiter nearby. I "lost on time" because I forgot to stop the clock. The arbiter came and declared a game lost for me because of time. Stupid logic, but here we go with the rules...

in a real tournament it would still count as a loss towards you because the position isn't drawn enough.
Questionable. I don't see that White made any progress during the last 50 moves. So a 10.2. claim should suffice to net the draw.
In FIDE laws appendix B for blitz:
"Article 10.2 and Appendix A.4.c do not apply."
So winning purely on time is just fine.
I was assuming that "real tournament" refered to standard chess. So I was refering to slow chess here...
Yesterday, I ended up with this position as black in a blitz game.
I had around 30 seconds left, my opponent around 90s. S/he declined my draw offer and continued moving around the rook, and occasionally a pawn to avoid a 50 moves draw claim. After about 50 more moves, I eventually lost on time in this position:
I know it's all according to the rules. But I would feel kind of stupid just moving my rook around for a minute just to burn my opponent's time. What is your policy? Do you think it is ethically justified to win like that? I am just curious about hearing other opinions.