The lining in question is very thin (akin to a layer of paint) and just burns up when the cans are re-melted.
Recycling beer bottles is indeed pretty easy once you get them to the processing center intact, but it’s getting there that’s the hard part. They’re fragile, pretty heavy and don’t stack well unless you put them in some form of packaging.
Once they’re broken, they’re basically useless; glass isn’t recycled much except as grit material for sandpaper; re-melting it is resource-intensive and sensitive to impurities.