Switched reluctance motor with rotating windings?
Yes. But it would cost you a commuatator, or slip rings and some switching electronics.

Do you know why a switched reluctance motor is the way round it is? It's so that the difficult bit, the rotor, that requires strength to not fall apart when spinning, and balance so it doesn't wobble when spinning, is made of a single strong material. If you want to make the windings spin (it's not impossible, plenty of motors do it) then you have to be much more careful and conservative with the manufacturing, and you sacrifice the simplicity of the stationary windings.