A new NiMH battery will likely last 7-8 years. Consider your 5 v board may fail at any time then you have a BCR with no place to put it.
FWIW I just picked up a PS2 5 v engine from 2001. It had a white battery which may have been original as the engine was used for display only. It measured about .6v and was replaced with a NiMH battery I had. I decided to try and see if the old battery would take a charge and was surprised it did. Its been holding for a week. I don’t plan to use it but it could be used in a pinch.
Pete