I imagine they would if they could, but it would be dependant on screening rights.
The Vicar of Dibley is currently available on Netflix meaning that the BBC wouldn’t to be able to screen it as Netflix would have paid for exclusive screening rights for a set duration. Renting screening rights to streaming companies is one of the vital revenue incomes to ensure they can keep our BBC license fee to a reasonable rate, considering they are creating content for a small viewer audience across, news in print, screen and radio, television, documentaries, drama, comedy, etc etc. I think people have been bashing the BBC for far too long, they produce wonderful content that punches above it’s weight compared to the mega budgets of American and foreign media companies.
I agree re reruns as i’d love it too, but their hands maybe already tied before the pandemic.