Me personally I would say that removing and have them show up after an ending adds more probability and might lead to more time spent blindly running the game over and over in effort to find more endings or badges when there could be none, it could be nice to have an achievement page but then that would also raise more question for more addition each and after update/s.
In my opinion i like them, theyre nice to know when you completed the whole game and there isnt any other endings to do.
If you insist on not keeping them there and having the pop up method, maybe adding something like after you get every badge you get a 100% badge or something that symbols full completion so people for sure know that there isnt any more left to do.