You can be nice, just make sure you think about what you're actually doing before doing it.
Letting a car go in front in the situation above: you're probably causing an accident.
Letting a car go in heavy traffic when there's one lane each way and everyone's stopped already anyway: won't cost you much time and you've allowed that person to move on with their life instead of being permanently stuck at an intersection he's never going to be able to get out of unless someone yields.
I live close to a few intersections where if no one is nice and yields, it's impossible to join unless you barge your way in and hope people stop. But to be fair, these aren't designed like death traps like the one above.
Driving is one of those things where we're supposed to be human - make choices, act sensibly, think about what we're doing and adapt to others around us. But often people assume it's something entirely deterministic - "if the light is green I'm going to launch forward even if there's still traffic moving past me and I'm going to get hit or hit someone, because green means I HAVE to go".
Being polite to others, asides from the nicety of it, is often more positive to everyone on the road than going "I have the right of way so I won't let anyone in" and allows traffic as a whole to move with less issues. But some people go way too hard on the mentality that every road user other than them is stupid and stop acting like humans because they assume others won't be able to cope. Which usually complicates traffic for everyone.
There's a roundabout in my daily commute in which at the end of the afternoon 80% of drivers are coming from and going to the same direction and there's usually heavy traffic in that specific direction that blocks the roundabout. Often, drivers who are approaching the roundabout to go to a different direction will signal their intention, and users already inside the roundabout will give way - even if they technically have the right of way and don't have to - because those users aren't going their direction and will only increase the number of cars stuck if they're not allowed through. Roundabout users being polite effectively makes traffic as a whole go more smoothly and everyone benefits. Sometimes someone inside the roundabout will be an ass and not let people through - and the result is always that everyone is stuck for more time because there are now cars inside the roundabout which could've already vacated it which are stuck behind someone who could easily let them through.
xkcd #2932: Driving PSA ( imgs.xkcd.com )
https://xkcd.com/2932...