I agree with the idea that a capitalist society should work harder than we do to price in externalities in order to fulfill the social value of a free market.
As a counter example to it being the only way though is how the modern world has drastically reduced and now culturally shuns (although we still have things to fix) human slavery without doing it via economic sanctions or price regulation.
I don't actually have any hope here though - politically in the US I see more of a slide away from free markets and toward techno-feudalism and culturally in the US I see a backslide in empathy and personal values people are willing to make sacrifices for.
You can't regulate people into having particular values (for good or for ill).
https://www.bankofengland.co.uk/working-paper/2022/the-colle....
But in any case I don't think turning consumption into something moral will ever scale. If you want to curb consumption you have to price in the externalities. This is true for everything - fast fashion and cheap flights too.
I don't think it is cultural - my point is that as someone who appreciates food for more than just sustenance you'll never convince me that tempeh/tofu/jack fruit/bugs will one day make me forget that meat is delicious.
I will gladly vote with my wallet or blood sweat & tears to continue eating meat especially if it becomes sustainable via price hikes. And I don't say this from a position of arrogance - I'm saying that I would cut many many many other things out of my life before I gave up meat due to affordability issues.