What component provides the bulk of the current in a buck converter? the capacitor or the inductor?
tl; dr: the inductor is the primary energy transfer element. The capacitor lowers the power rail impedance for both phases of switching and thus reduces output ripple.
A buck regulator with an inductor has two phases:

Charging: current is being poured into the inductor, flux is increasing. Current flows from the power source, through the upper switch, through the inductor and into the load and filter cap.

Discharging: inductor is dumping current, flux is decreasing. Current flows from the inductor, into the load and back through ground and through low side switch or catch diode back to the inductor.


So it’s pretty safe to say that the inductor is being used as the energy transfer medium. Its stored energy is in the form of flux, and it’s being alternately refreshed from the source and dumped into the load. It’s doing the bulk of the work.
The filter cap has far less dynamic current variation than the inductor. It's bypassing the triangular ripple current from the inductor, which in a properly tuned buck should be about 30% of the max current. If anything, it’s the input cap before the high side switch that’s really getting the workout: it has a very large dI/dt when the high side FET turns on.
In your sim, try using more reasonable values like say 10uH and 100uF for the filter cap. Also, model the cap and inductor with series resistances to more closely reflect actual components. Finally, add that input cap, again with series resistance. Also, you can set the FET ‘beta’ in Falstad, use about 15 for the switch.
BONUS: here's a constant-on-time type buck that delivers 6A at over 90% efficiency (at least as far as Falstad is concerned.)

Simulate it here