How long has the method been there? And does it hurt anything for it to be exposed? Removing it at this point may break code if it predates Python 3.7.
From looking at the git blame this is there since 2006. Maybe this should be dependent on issue #30262. Maybe at first there should be a deprecation warning and then removing this later. I understand that this might break someone's code but this is an undocumented method of an undocumented class in the sqlite3 module. I don't think that there will be a lot of people that use the sqlite3.Cache object.
With over 10 years of existence for that method, I can guarantee you someone relies on it, and so we should do a reasonable job to avoid breaking them without at least some warning first.