Is it worth buying a pizza stone...?
Yes. Stone, steel, whatever. Thermal mass.
The objective with many styles of pizza is to have thermal mass so your dough will start baking immediately after you put it in the oven. Pans and screens do not have thermal mass. With pans and screens, your dough doesn't really start baking until the pan or screen gets hot, which may be a couple minutes after you put it in the oven. It can make a big difference.
I use a stone even when I use pans because a hot stone transfers heat to pans much faster than hot air transfers heat to pans. (Reach into a hot oven. It's bearable, right? Now touch the hot stone, or even a hot rack. See how it immediately starts baking your hand? Same thing with pizza.)