But most of the European political elite want to unite the continent under a single government instead. Given that, the best kind of Brexit would be one where the UK is no longer a part of this, and can sign various unlinked bilateral treaties to continue cooperation in the areas where there is agreement, and discontinue in areas where there are disagreement.

This makes perfect sense - agreement on everything is rarely possible, so collaboration on the areas where people do agree is the best you can do. It's also exactly what the UK has proposed repeatedly. However the EU refuses to allow it, exactly because if people were offered that alternative the EU and associated gravy train would cease to exist tomorrow.