>>719921717 (OP)
The game's entire theme is how allegiances don't matter and soldiers are pawns to be used and discarded when they're no longer convenient.
The Cobra Unit is an antiquated squad of old men with no country that wants them and nowhere to die other than on the battlefield. They're mostly happy to follow their leader into one last battle where they can finally be put to rest.
On a more meta level, they know they're testing The Boss's new apprentice, and future games (PO, PW, 4, V) show how The Boss put her hope in Big Boss to change the status quo, something he mostly succeeded in.