Smaller size of radiator requires higher field strength in order to compensate smaller size.
Ferrite core antenna uses resonance effect in order to accumulate energy of field strength oscillations for a specific resonant frequency. The same effect happens when small size resonant antenna working for transmission.
Regarding to rotating magnet, if it has high enough field strength, you will be able to listen it on receiver. But the problem here is that it will produce clean carrier (clean sine). It will be hard to apply modulation for a rotating magnet.