Your example was extreme with the 'running them off the road' bit, but actually meditation isn't helpful unless it pushes you to that breaking point.
You need to get worked up, speak your mind, start the argument, quit your job when things get too bad. Life isn't a float on the lazy river. Feelings of anger and pain exist for a reason.
Thats why meditation, as it's sold, is bullsh*t. You're describing an alternative to xanax.
I've noticed a lot of people that meditate struggle with aversion of thoughts and feelings vs "letting go" of thoughts and feelings. You certainly feel every bit of pain, anger, and sadness as a non meditator would.
The distinction is that you work on "meta-cognitive awareness". You try to avoid getting swept up in the narrative thought stream if possible. So here goes from my own experience (doesn't work 100% of the time).
without mindful awareness
Guy cuts me off -> "WTF is that guy doing? What a moron! Someone always has to mess with me! Look at how smug he is. I want to jam his nose into the back of his head"
with
Guy cuts me off -> "WTF is that guy doing? Woah feeling that anger. I can feel it right in my chest and kind of a warm feeling in my face and arms. Hmm interesting. I wonder if he is rushing to the hospital or to some emergency. Just like me, I've accidentally cut someone off before. Oh well what's on the radio"
It helps you build more mature mental models. Mental models are useful but often wrong. Mindfulness can help you question your own mental models and take things less personally. Tons of reputable studies will back up mindfulness and meditation as a standalone or complementary tool for stress, anxiety, depression, and pain. Medication still plays a very important role.
Edit: Upvote to you for bringing up a good point. It is very hard to sort out the bull*hit in the meditation community. There is an awful lot of tradition, psudo-science, and plain old snobbery in this community. Anyone that gets involved should start with the basics and avoid as much of the spiritual hype as possible.
You don't always have the power to change things. Change the things when you can, yeah, but if you are stuck in traffic, in a boring meeting, in a job you can't quit now, then maybe meditation is a good idea. You can at least not hate your life while you find alternatives.
I mean, I find specially hard to improve myself at my job if I hate it, and so it will be harder for me to find somewhere else better. If I'm mindful, I will actually keep working hard, learning, and I will separate myself from the bad feelings. That doesn't mean I will stop searching for alternatives.
You become more aware of the unpleasantness of bad situations through meditation not less. You are just less reactive. In fact, you might take action much earlier on because things wouldn't have to reach a boiling point to make you really take note.
So, here's the thing. You need to make an important sale. Is the best way to prepare for it to get more angry? Is quitting your job without having another lined up what you'd consider a winning move?
There are times where being angry actually helps, but they're a lot less common in the modern world. Usually, it will screw you over. (For example, getting angry in traffic is utterly useless.) Starting that argument because you're angry makes it unlikely that you'll actually persuade anyone.
You'll make a better case if you're calm about it and can think clearly. How do you do that? Meditation is one way.
You need to get worked up, speak your mind, start the argument, quit your job when things get too bad. Life isn't a float on the lazy river. Feelings of anger and pain exist for a reason.
Thats why meditation, as it's sold, is bullsh*t. You're describing an alternative to xanax.