Buck converter operating frequency range:

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!

The fact that a compensation pin exists lets you tailor your compensator to meet certain design goals: a specific crossover frequency (the point at which the loop-gain magnitude crosses the 0-dB axis), phase and gain margins. You know that the frequency response of a switching converter is affected by parasitic elements like \$r_C\$ the capacitor equivalent series resistance (ESR) which introduces a zero for instance. So when then the compensation is internal (like with a 3-pin linear regulator for instance), then you may have conditions on these stray elements for which the stability is ensured or not. It is your role then to pick the right passive component and make sure its parasitics match the manufacturer recommendations.

On the other hand, if the comp pin is available, then you can choose the compensation strategy to neutralize the effects of the parasitics knowing that they will move between known boundaries during the converter lifetime. You can also tailor the transient response you can accept (fast response with overshoot then moderate phase margin, sluggish response but 0 overshoot with higher phase margin) by selecting where to place poles and zeros.

A lot of ICs integrate operational transconductance amplifiers (OTAs) for design reasons (small die area etc.) but I don't like them especially if you are about to implement a type-3 compensator (1 pole at origin, 2 zeros and 2 poles). As highlighted here, you see that depending on the division ratio between \$V_{out}\$ and \$V_{ref}\$ you are limited in spreading one of the pole/zero pair and cannot boost the phase as much as you would like to. Also, in an OTA, the transconductance \$g_m\$ enters the picture as well as the resistive ratio fixing \$V_{out}\$.

Regarding the MC34063, it is a hysteretic controller inherently instable and does not need to be compensated. It can be extremely noisy as the bunch recurrence can enter the audible range at high peak currents. I think it has been released by MOT after Signetics introduced the µA78S40: yes, some years ago : )