I have been working my way towards making stovetop pizza, and I just made my first thing that I think could be reasonably so described.
My first experiments were with storebought frozen pizza dough, just trying to cook the dough in a frying pan, not trying to actually make pizza. After thawing it, I separated off a reasonable-sized portion and made it flat(ish). I put olive oil in a frying pan, put my circle of dough on that, and drizzled olive oil on top too, put a lid on to keep the heat in so the top would cook better, and cooked it somewhere between low and medium, and turned it over when the top started to look cooked-ish. I did this with various thicknesses of dough and various temperatures and it took varying lengths of time but lots of options worked. I mostly ended up settling on a temperature just below my stove's medium, for about 10 minutes on one side and about 4-5 on the other. A few times I actually rolled the dough out on a floured surface, but more often I just pulled it roughly into a lumpy circle with my hands because that was easier for me.
Part of the motivation for this was in the summer, wanting to make fresh yeast bread without having to run the oven.
At some point I started making my own no-knead pizza dough, a half-recipe of
this (using about a third of it per occasion, and saving the rest to cook later).
Earlier this week I tried rolling the dough out, putting cheese on one side, and folding the other half over and sealing up the edges. It almost worked but I put too much cheese in and the seal leaked and it seemed a bit greasy with the combination of all the cheese and the amount of oil I cooked it in. I think the concept is fine and could work (with other fillings than just cheese as well) but the implementation would need some tweaking.
Today I went back to just dough stretched out in my hands, cooked it on one side like normal, flipped it over like normal, and then spread some storebought pizza sauce on it and laid out some cheddar cheese on top, put the lid back on, and cooked until the bottom was done and the cheese was melted. It would probably be better with a more pizza-y cheese, and there's certainly room for more toppings, but the concept worked!