That doesn’t make the phrase useful. It’s a catch-all phrase, often dropped without any arguments backing it up, vilifying any change to any working system.
There are good reasons why you sometimes really shouldn’t change working systems (you mentioned one), but then you shouldn’t use that phrase and leave it at that. Say something like “Changing the system in the proposed way at this time would be bad because of reasons A, B and C.” or something similar. Don’t take “If it ain’t broke, don’t fix it!” as a self-evident truth.
There are good reasons why you sometimes really shouldn’t change working systems (you mentioned one), but then you shouldn’t use that phrase and leave it at that. Say something like “Changing the system in the proposed way at this time would be bad because of reasons A, B and C.” or something similar. Don’t take “If it ain’t broke, don’t fix it!” as a self-evident truth.