Will adding something like a pizza stone smooth out the highs and lows of an oven's cycling (the switching the element off and on)?
I've used pizza stones to even out fluctuations in two different ovens which had severe on/off temperature cycles. One oven was an older gas oven, and the other one an older electric oven. In both cases, installing the pizza stones did indeed lower the amount of temperature fluctuation in the oven; in the electric oven, fluctuations went from +/-45F to +/-20F, which helped a great deal with cooking times.
For this to work, the pizza stone needs to be sufficiently massive to act as a heat sink; each of the stones I used were over 15lbs. This will also cause the oven to take longer to heat up.
Pizza stones will also help even out random hot spots created by a bottom flame or element, but as @dbmag remarks, they won't do much, if anything, about top-to-bottom gradient.
It will go some way to reducing the temperature fluctuations, and is usually done to mitigate the sudden temperature drop caused by opening the oven door when making something that wants a high temperature like a pizza.
The consequences of the oven cycling on and off tend to be felt more in terms of placement within an oven; if the heating element is at the top of the oven, say, then food at the top is more exposed to periods of high temperature. That wouldn't be necessarily resolved using a stone.
The fact that this isn't a common practice for everyday cooking, whereas other techniques like putting food on the middle shelf or covering with foil are common, suggests that there's not much need for this. But if you suspect the cycles are causing you a problem then by all means give it a go.