To make money from their books etc..? St Peters in Venice is the same. Didn't go in there either. Not sure if flashlights damage the artwork? I visit smaller churches in London & Westminster Cathedral. Southwark Cathedral charges £4.
I can understand why they ask for a "contribution". One reason why i visit London churches. They don't charge and allow photography. I always give a donation and pay for leaflets etc.. I find visiting churches sometimes irritating though. I won't bore you with the details!