Let´s assume I use a synchronous buck converter switching at 1MHz and a 47µF MLCC at its output whose self-resonance frequency is right at 1MHz.
For my understanding, using an DC/DC converter output capacitor near or at its self-resonance frequency is not a bad idea. But I am not sure. I think, there should not be instability issues as long as the resonance frequency of the inductor/capacitor combination is well above or below the 1MHz. So, for 47uF and 2.2µH, I have resonance near f = 15kHz, which should be fine.
Is the "loss" or even "turnover" of the phaseshift of the capacitor a problem in that situation? I should note, that the converter uses constant frequency PWM and (as far as I can deduce from the block diagram below) peak-current mode control.