In speed games it's all about the clock from the beginning. So to win on time in a drawn (or losing) position is part of the strategy.
In untimed games I will play on in a drawn position vs a weaker player and basically wait for them to make a mistake. I may know it's drawn, but I want to see if they know why it's a draw.
It happened to me (but I'm sure also to you) on few online endgames almost certainly draws, the opponent did not accept the invitation and continued to play focusing on the psychology factor / time/ or nerve to overcome me. Obviously it's part of the game and anyone is legitimate to do this but I think it denotes great pettiness and poor sportsmanship from these players.
It 'a shame to spoil those games that were beautiful and hard-fought with such childish attitudes. I do not think it will prove you are the best chess players in this way.
It's not just a matter of winning a game or two, it' how you win that it's also very important.
In chess, sports and also between ancient time warriors ethics and respect were and are part of the greatness of a player, or an athlete, something that many of today Internet alleged chess players would do well not to forget. What do you think?