Yup, exactly. Compare the price of a PC power supply, which outputs a very smooth constant voltage, to a microwave oven. The microwave oven is cheaper, and uses all 1800W of your circuit. A DC power supply that does that is much more expensive.
It is truly amazing how cost-optimized microwave ovens are.
So the transformer based microwave oven power supplies have a 2.2kV transformer and then double that to 4.4kV for the magnetron.
There is no filtering or smoothing, as those parts would cost money and present a danger to the service technician.
So the voltage feeding the magnetron is not even sinusoidal.