IME, sound barriers don't help that much unless the house is literally next to/behind it. Sure, it may help a little, take the edge off engine revving, but the noise will still be there. Next time you see a sound barrier, go check out the street on the other side and see if it's enough for you.
My understanding is the majority of people acclimate somewhat to loud noises. For example, people who live near trains say that after a few months they hardly notice it.
But you have to know yourself. For me, it would constantly get on my nerves. I might even get more sensitive to the noise the longer it bothers me.
But there is also evidence that, even for those who are not consciously bothered by the noise, it has hidden negative physical and psychological effects. For example, heart rate/cortisol increase even while sleeping. Not worth it to me.
Air quality is also proven to be terrible near freeways. Within 200-500 feet, say. Not just emissions, mostly brake and tire dust particulates. Even EV will not solve that issue
As you can tell, I'm cranky well beyond my years. Now get off my median strip.