This is a little incomplete... using a resistor divider or a variac ("halfway" switch) is not the only way to limit current -- switched mode power supplies (AC/DC or DC/DC converters) can limit current and/or voltage to arbitrary, programmable levels with efficiencies of as high as 98% (eg only 2% of energy lost as heat). They turn the output all the way on and all the way off according to a clock signal, with feedback loops connected to sensors at the output to regulate the output voltage or current.

It's still pulse modulation, just done really fast. So instead of using bang-bang at multi-second intervals, you do it at millisecond intervals (or in a modern DC/DC converter, down to ~500 nanosecond intervals)

Why this is not done on a hob/electric stovetop is purely a cost of manufacturing thing. There are solid-state relays that can switch 10 amps and reasonable service lifetimes but they cost $10+ each, and require implementing electronic controls (eg you have to use touch-buttons to set the heat level, or have analog-digital converters reading a rotary knob position...) and various other components, like needing to address current leakage from the solid-state-relay when it's off. The general guideline is you can expect retail value of a piece of electronics to be about 3x the component costs, so for a 4 burner stove it'd likely add at least $150 to the retail price. The benefit to the consumer is almost nil, so justifying the extra cost and complexity is not worth it.

I've actually seen quite a few induction cook-tops that have bang-bang control. Which I don't really understand if they're using switching topologies, like you say. But maybe it's still cheaper to just disable the transistors entirely than to have to design around a variable frequency switching controller?