The square thread is not very practical for screwing back and finding the right alignment. Also the very thin border of the cap has not very much surface to be hold safely for screwing in.

For undoing a corroded battery you might drill a tiny hole in the bottom and use a screw for wood like a corkscrew. If the second cell is also stuck then you may get hold on a longer drill and longer screw or use a sort of extension. My grandfather has brazed a drill into a piece of tube for such application.

Everything is worth to be repaired! My son came with his EarPods and broken wire at the plug and after googling and finding the right pin-out he was happy that he learned how they can be fixed. It was not all about some saved bucks but having a great hour+ with my son, having fun and learn something useful. Not soldering in particular but co-work of old school and new age :-)

Besides that each repair is actively saving energy.

Today I managed to repair a broken plug of Earbuds. The speciality is the Microphone cable, which comprises a golden cable which is surrounded by red and green stranded wires.