Why SSRs for heaters?
It's not very different from why you always have solid state switches and never electromechanical relays for variable speed motor drives.

A electromechanical relay can only ever be 100% on and 100% off with nothing in between, and it can't do anything about it because it can't switch fast enough and it can't switch very many times before it completely wears out.

As a result, a mechanical relay can only turn on when the element is too cold and turn off when the element is too hot. (Think your house thermostat or your toaster oven where it turns on for some period of time, then turn off another period of time with the temperature fluctuating wildly). All you can do is hysteresis control. You can't do PID because all you have are off and on.

Technically an SSR can also only ever be 100% on or 100% off too, but SSRs do not wear every time you switch them and they can switch fast. Therefore, you can switch it fast enough and often enough that you can simulate something like running the heating element continuously at 50% power and keep the temperature range of the heating element nice and tight.

An SSR can switch dozens or hundreds of times per second without wearing out so it can keep the heating element in a much tighter temperature range essentially making it a variable temperature element.