No, it would be silly to take away those extras your primary school offers, Mollygo, just because others in the sector don't or can't provide them. I am not being patronising when I say that state primaries usually do a great job delivering the best possible all round education with the little they have. We should celebrate that while making improvements to those who struggle. My DGS does gardening, cookery and first aid at his state school, all done on a shoestring with enthusiastic teachers and parents. Sometimes where there's a will, there's a way, especially in non academic areas, despite the lack of funding.
Often independent schools, for a small fee, let out their premises to local sports clubs, to societies and to groups, and for summer clubs. If that facility were not available, then these people would have to travel long, costly distances to find a swimming pool, cricket pitches or a fully equipped kitchen etc, especially when these are being closed down or are already fully booked. There is a case for private schools to provide and share with the local community, it's not crumbs from a table, it's a practical and sensible solution.