Yes, basically those are cheaper because they use less ressource and thus have necessarily less environmental impact. It doesn't make sense any other way.
Capitalism has plenty of bad outcomes, but inefficient use of ressources not generally one of them.
All of this makes it very hard for people who are posturing trying to appear virtuous/moral in their choices (food, clothing, whatever). At the end of the day if you think you are a problem the best solution is to get rid of it...
All the studies about plant-based vs animal food are deeply flawed because they don't compare properly the nutritional profile and ressource intensity.
Most of what we feed to animals is waste/byproducts or just not fit for human consumption, but conveniently can be grown in less arable land.