CrossRoads:
PWM at any speed is not good with relays. The contacts are usually rated for so many closures, which PWM would quickly wear out, and the chattering would drive one mad as well.
Crossroads, thank you for the help but please allow me to quibble re: the above. Many appliances feature relays being used in a PWM manner. Whether its cooktops, ovens, clothes dryers, or microwave ovens, large loads are still predominantly switched using relays in the white goods industry. However, that's not to say that Triacs and similar solid state devices that allow faster PWM without the chatter you describe are not used, far from it.
The electric cooktops of a client of mine started using solid state switching devices in 1999, there is a Triac for suction control in our Kenmore canister vacuum cleaner, and variable-speed drives are also quite common for motors / compressors in clothes washers, dishwashers, mini-split AC systems, and even refrigerators.
These days its not uncommon to find appliances that feature both solid state as well as electro-mechanical switching systems. Some things like LEDs get dedicated LED driver chips to enable dimming, multi-color displays, etc. while larger loads that do not require speed control still predominantly use relays. Some appliances like microwave may feature a couple of small Triacs for small loads in addition to larger electro-mechanical relays for the magnetron power supply and other loads.
I expect more and more solid state relays being used in appliances as time goes on, driven by the dropping costs for solid state options and the features that can be added to appliances through their use. Years ago, a variable-speed motor in a vacuum cleaner would have been realized with multiple speed taps and a bank of relays or a high-power selecting switch, today it's done some pushbuttons, a Attiny, and one Triac. The soaring cost of commodities (such as the additional power lines required for the old approach) vs. the dropping costs of and greater familiarity with solid state devices presumably had something to do with that.
Thus, both types of power switching technologies currently find their application in high- and low-power switching situations, with and without PWM. As I see it, the most applicable solution depends on many factors and it wasn't clear to me just what the application was going to be, i.e. the magnitude of the load being switched, the speed requirements / duty cycle for the PWM, etc. Thanks again for all you do for the community!