Chess with a 5 minute base time and no increments is a very different game from chess with a 3 minute base time and 2 second increments. It probably always had a winner and a loser except for when there's a stalemate. The challenge pretty much is to form a clear plan on how to quickly react to each move your opponent could make and not get checkmated before your opponent's time goes to zero so that if your opponent is slow enough, you can win by moving faster than them and waiting until they run out of time.
Chess with a 5 minute base time and no increments is a very different game from chess with a 3 minute base time and 2 second increments.
No, it isn't. Most of the moves in the two formats are played with the same aims and with the same mindset. Most games are decided before time becomes an issue. Only if the game is still undecided with little time left on the clocks does the increment make a difference.
In 5+0 flagging your opponent becomes an option based purely on time rather than position. You can have a completely even position but the player with a few seconds left will lose to the player with 30+ seconds left purely and simply because he can't move quickly enough and not for any chess reasons. In the same position in a 3+2 game that is not the case. Two seconds is ample time to make a move. Flagging still occurs, of course, but it is based on chess skill and ability. The player losing on time just can't solve the problems the other player sets him in the limited time available.
It probably always had a winner and a loser except for when there's a stalemate.
This is just wrong. Many games in 5+0 result in draws because of repetition or perpetual check. They can also result in draws by agreement because neither side can see any winning chances, both players are short of time and neither player wants a lottery.
Timothy, do you actually play much chess? Because your questions are full of wrong assumptions which a regular player of the game would not make.
3:2 allows for the ability to gain time especially in online chess as you are able to perform pre-moves you can catch up quite a lot of time. I've once played a game where my opponent tried to flag me in a 3:2 game and then accused me of cheating - Never underestimate the incremental time!
See Wikipedia's page on Timing-methods