You absolutely wait until about 5 seconds left to take your shot. You want to take the last shot of the game.
But we were down by 2. The goal there is to tie the game. Whether there are 20 seconds left or 2 that is the goal. It's actually better to shoot it earlier in that situation in case we miss and then have to foul, hope they miss a free throw, etc. If you wait and take a shot at the buzzer, a) it will probably be a worse shot because similar to end of shot clock, you're rushed and the defense knows exactly when the shot is coming, and b) if you miss the game is over.
When you're losing the ideal strategy has to be to score and then get a stop. If it's tied, then the strategy is to take the last shot