Is there a good free circuit simulator (that use a schematic as interface, I assume)?

I somewhat agree with you in general though—if the web UX is a breadboard… maybe just get a breadboard? At the same time, while physical parts are generally cheap enough, power supplies, multimeters, an oscilloscope… that part of the hobby can add up.

Sometimes too I am waiting a week or two for a part to arrive from Mouser, it is nice to be able to mock up a circuit online.

There are many. What's your (computing) platform and what are you trying to simulate? The more professional tools (beginning with freebies like LTspice) are oriented around letting you probe waveforms from simulated inputs and are not as oriented towards interactive probing "does this LED light when I press that button?" as a hobbyist might want.

There are tons of free sim tools. 'Spice' (Simulation Program with Integrated Circuit Emphasis) was a very early commercial sim. So many of the free ones use some variant of spice in their name. LTSpice, Qspice, etc.

Kicad is an excellent free schematic capture and simulation software.