The biggest advantage SSRs have is that they can operate fast. The also usually switch at the zero-crossing point of the AC cycle which gives everything else in the circuit a pretty easy time.
I'm assuming you are thinking in terms of HT ovens here. For the speed issue, it helps to consider what is going on when at temperature.
The controller cannot usually modulate the wattage of the elements. If you have 3000W of elements, they are outputting 3000 Watts when powered and nothing when unpowered. The controller has an output cycle time and powers the elements for a variable proportion of this cycle time in order to achieve an effective output somewhere between zero and 100%. If the power needed is 50% (1500W in our 3000W example), the elements are on for half the output cycle time and off for the other half.
While the elements are powered and putting out 3000W, the temperature rises. While they are off, the temperature falls. A trace of temperature against time would show saw teeth.
If the output cycle time is long, the saw teeth will be large. If the output cycle time is short, the saw teeth will be small. The smaller the saw teeth, the more stable the temperature.
For pottery kilns, a 30-second output cycle is not uncommon and electromechanical relays have no problem cycling at this rate. For a HT oven though, a 2-second output cycle time is quite common and this is too fast to be continuously cycling a contactor (a contactor is basically a high-current relay)