I just wanted to offer a little more insight in case you are interested. Your thought was not entirely false.
Household dimmers and fan speed controllers don’t actually lower the voltage evenly across the whole waveform, they just kinda chop it up. The integral, power delivered to a constant load, lowers, but that is due to a funky-looking ugly-ass waveform.
Lots of fans we use in our hobby can be run with a speed controller that lowers the effective RMS power by chopping the waveform either on the “up”, or on the “down”, with either a TRIAC or an SCR. They will, however, not be very efficient, noisy, and you can only slow them down so much before they start overheating and being nasty and unhealthy, as @anon32470837 stated. Bathroom fan speed controllers are the same, just lowering power, effectively. HOWEVER, if you were to measure such a controller’s output with an RMS voltmeter under load, it would read lower voltage. So your response has basis, most household motors are controlled kinda like lowering voltage, but only to a point.
The best way to control a motor’s speed is by varying frequency as well as voltage, maintaining the same voltage to frequency ratio. And those doo-dads are hella expensive… they have a bridge rectifier, a converter, and then an inverter. And they all work together to match the load, not speed. Pretty cool stuff, and only been around since the mid-80s. They are called Variable Frequency Drives (VFDs). If you have a fancy washing machine or a dishwasher, it’ll have some in there. That’s why the bastards cost so much.
The drivers in many LED replacement bulbs have been designed to accept chopped power, both as a source, and as a reference for desired diode output. These can charge internal capacitors sufficiently from the supply, and release as needed into the diode board. Some do it better than others, which is why we have two types of dimmers - forward-phase control and reverse-phase control. Some drivers’ design works better with the latter part of the sine wave chopped rather than the earlier.
/stoned rant
HH