In the ends of most games, one team is ahead by a varying amount of points. When this happens, the losing team starts doing a full court man to man press. Wouldn't it be logical for both teams to press at the end of the game, for the winning team, they could try to put some more pressure on their opponents, while the losing team is hoping to create a turnover and quickly score. Wouldn't it be better for the winning team to press as well, although pretty loosely. While still applying pressure, they could get back on D if the opposing team beats the press. Why would coaches not do this, if they wanted to play safer, they could do more of a loose press, then pick up the intensity after the opposing team comes over half-court, and it would be a good practice for critical in game situations when they are down.
I am not an expert, but I think if you are winning towards the end of the game your approach is to cause both you and your opponent to have possessions run as long as possible. When your opponent has possession a press defense exposes your team to a long pass and a quick score. Setting up your half-court defense instead causes your opponent to choose between a quick, lower-chance shot or a slow-to-develop, higher-chance shot.
If you are up in a game the last thing you want to introduce is variance in scoring.
You have to understand that in the NBA there are very few players that are out of shape, they can almost all make a 30 foot pass easily, and most are very adept dribblers. The press is a good strategy when your opponent is slower, not in good shape, or has poor dribblers. Hardly ever a go to strategy in the NBA. The risk is far greater than the reward and that is why you only see it done by teams losing at the end of games.
The other factor for the winning team isn't just giving up quick points but in the NBA whether it is fast break or press (which ends up into a lot of "fast breakish" 2 on 1s or 3 on 2s), these things have ended in a lot of open 3s. This is a departure from 10-15 years ago when coaches pushed their players to take the ball hard to the hoop on fast breaks.
Then layer on if the winning team presses, the losing team beats press for easy bucket, the winning team is now in a worse position to beat the losing team's press. Remember you have 3-4 guys pressing so now who is going to help beat the press? (NBA has 8 second half court violation)