>The animal was fed something we could have eaten

Not necessarily - I don't know about where you're from, but here our cows and sheep eat grass and live in fields that wouldn't be suitable for crops

Research is underway to process grass into a milk-substitute. It's a matter of making microorganisms that create the right mix of proteins from ground grass. Plenty of food is already created this way. E.g. microbial rennet is made up from proteolytic enzymes grown in a fermentor and natural (as opposed to chemical) vanillin can be made by a microbe.

If you select meat marked with (certain? most?) eco labels the animals are mostly fed grass or similar.

I tried finding the English page corresponding to https://www.wwf.se/mat-och-jordbruk/kottguiden/ekologiskt-no... but failed ¯\_(ツ)_/¯