"........... While the fact that the Nikon lens mount won't accommodate other-brand lenses, ........"
That is NOT TRUE!
There are several third party lens (Brands)manufacturers (Sigma, Tamron, Tokina, Zeiss) that make lenses with the Nikon F mount that work perfectly on the D5200 or any other Nikon DSLR. See my post above for the third party lenses that fully support AF when mounted on the D5200. Good Luck and Enjoy your Nikons!