I hate to break it you but an old 50s era stove works exactly as the GP describes - there certainly wasn’t low cost high power solid state power conversion circuitry in those days - the mechanism is extremely simple, an adjustable bimetal thermostat that can turn the element full on and off with adjustable duty cycle - and that modulation frequency is over seconds. Any smoothing of this mechanism is inherent in the thermal capacity of the heating element.

And this is modulation of current - think of it as a very slow PWM.

If it's modulating as you describe, it's completely imperceptible, unlike any of the other ones I've had to live with in SF bay area apartments.

But I must admit I have not disassembled the thing to understand its workings.

I don't even bother with heavy copper-clad pots and pans anymore, which were necessary before. This thing behaves like a gas stove.

So it's the heating element thermal inertia that differs, to smooth out the temperature?

Edit:

Looking at [0], what you're describing seems to be known as an "infinite switch".

That's not what the old stoves like mine has, this is just a rotary switch with 5 selectable presets. I assume it's changing the resistance.

Worth noting is also the even older Kalgoorlie [1] style stove, which changed the number of heating elements connected to regulate temperature.

This repair guide [2] describes both infinite and rotary switch controls on a high-level:

  When the heating element is on, the heater inside the switch is on. The bimetal heats
  (along with the element) until the contacts open. Then the bimetal cools (along with
  the elements) until the contacts close again.

  There are also fixed-temperature switches that vary the voltage going to the heating
  elements to maintain fixed, pre-set temperatures. These are usually push-button or
  rotary switches with fixed settings such as warm, low, medium and high.

  In fixed-temperature switch controls, heat levels are varied by applying different 
  voltages (110V or 220V) to different coils of different resistances.

[0] https://en.wikipedia.org/wiki/Infinite_switch

[1] https://en.wikipedia.org/wiki/Electric_stove#Kalgoorlie_Stov...

[2] https://www.appliancerepair.net/oven-repair-4.html

As you will see in the schematic of chapter 4 the fixed temp switches vary two voltage combinations (that you get “for free” with split phase power) and two coils to get the limited power levels. But this requires multiple coils per burner as noted. If it’s a single nichrome element per burner then even with fixed detents it may likely use a bimetal switch.

> I assume it's changing the resistance.

This isn’t feasible since you would need a resistor that was as big as the burner and essentially dropped as much heat as a stove element - for instance you would need a dummy load to dump as much waste heat as the burner itself to get a medium setting. In theory one could use a variac or multitap transformer - but again those would be relatively huge and heavy for the currents involved.