Choosing primary inductor and output capacitor values for a buck converter

I think the generalities are:

For a given frequency, ripple voltage and load current, higher inductance improves the losses in the switch, since the peak current gets closer to the load current as the inductance rises.

For a given frequency, ripple voltage and load current, the transient response (settling time after a step load or input voltage change) gets shorter as the inductance gets lower, since the inductor current changes more in a single cycle.

Those generalities do not imply that changing the frequency is not something you should also consider.

The larger the inductor, the greater the voltage spike if you suddenly disconnect the current (or the voltage drop if you suddenly increase the current drain). The larger the capacitor, the lower the voltage change.

To allow for sudden drops in current draw, it helps if 0.5*LI^2 is substantially less than 0.5*CV^2 (i.e. if the current drops to zero, you can dump all of the inductor's energy into the capacitor without a significant voltage increase).

For the case of the output current suddenly decreasing, you could just dump the energy into an overvoltage protection circuit if it's likely to be an infrequent occurrence (i.e. not a PWM load). For the case where the current suddenly increases, you can't increase the inductor current any faster than dI/dt = Vin/L, so any excess has to come from the capacitor.

tl;dr version: a lower L/C ratio = less voltage fluctuation for a given current fluctuation.

I believe that more inductance also implies a bigger inductor, because the amount of energy that you can store in a given volume of core is more or less constant. Higher inductance at a given current stores more energy in the core, so it requires a larger core to prevent saturation.