Let's look at the title question from the perspective of engine chess, which is more objective in the sense that you can get two engines to play tens of thousands of games against each other at whatever time control you desire.
If you look at the latest season of the unofficial world computer chess championship, you'll find that the strongest engine is Stockfish, and the weakest is Bagatur/A0lite. A match between the two engines on equal hardware & time control won't be much of a match - in a 100-game match I'd be surprised if Stockfish doesn't score 95% or more. The gap is just that large. Let that sink in for a moment: in an equal match, Stockfish is expected to win with both colors, again and again and again.
However, if you allowed Stockfish only 1 second a move while giving Bagatur/A0lite an hour a move, then it's no longer so certain that Stockfish will beat Bagatur/A0lite. In fact, it might very well lose. See the result of similar testing in the past, where Stockfish had only 0.3% of its opponent's time.
You can see the absurdity of it all. Let's say I sit down to play a blitz match with Bagatur against Stockfish at time controls of 5 minutes per game. Stockfish plays a move. I let Bagatur think for two days, then come back and make a move. Stockfish says I lost on time. I counter with "I flagged, but flagging isn't considered a win". If Stockfish were a human, how do you think it would respond?
tl; dr: the clock is part of the game. If you get a good position, but have to spend too much time to reach that good position, you might not be winning.