Self resonant frequency of buck converter
the controller should be designed in such a way that the controller
  bandwidth is higher than the circuit's self-oscillation frequency.


Well, for a 1 MHz switching converter (as an example), the LC circuit will have a resonant frequency that is probably no more than one-tenth of the switching frequency and quite possibly this could be one hundredth i.e. 10kHz.

Here's an example: -



I know it's not a straightforward buck regulator but it's still using a 6.8uH inductor and a 22uF output cap. Resonant frequency is 13 kHz and ripple should be pretty good.

So, to answer your question directly, I think you are getting muddled up!