It's nothing to do with damaging art work or not, I think it's wrong because it's a crucially important place of worship and those who care a lot about that, don't want photos inside it. Those are the rules. It's nobody's public "right" to take a photograph.
It's also the same in other religious places such as Westminster abbey.
And for sad reasons, it is also banned inside some exhibits at auschwitz. However when I was there, while groups were taking photos inside where the hair is 😔 They were told not to, and did anyway. Who the hell do they think they are?
It's just utterly disrespectful to take photos where it is not allowed. If you don't like it, don't go in the first place.
Or do what the rest of us do and just gaze in wonder (or horror) and internalise your memories. Trying to sneakily take photos of somewhere like the Sistine chapel is just pathetic and rather sad that people don't have confidence in their own memories.
And if you want to see what it's like again later, there are official photos which are much better than anything an amateur tourist can snap.
To me, it's a no brainer and I hope more places of importance ban snaps.