Good idea, but finding food grade stainless plate the size of a pizza oven may be a challenge.
Who said anything about stainless? The "baking steel" is just shot blasted A36 steel (like a restaurant griddle), that is oil seasoned just like a cast iron pot.
You just need something thick enough that it won't warp in the heat (say 1/4").
Speaking of cast iron, that's what I actually use in my oven. I used to use a cheap pizza stone, but after breaking two (and being annoyed by the round stone in a rectangular oven), I went in search of something better. I had actually considered slate, since I got a scrap pool table years ago and used the biggest piece to make my kitchen table, but I was afraid of it flaking in the heat (same with granite, and soapstone is too expensive).
Anyway, after looking at fibrament (the best stone solution I could find), I started to read up on the metal option. Pound for pound, cast iron holds twice as much heat as stone (higher specific heat), AND it conducts that heat much faster into what you're baking. Win/win.
Then I happened upon a large (almost 150lbs) slab of cast iron that used to be a restaurant griddle (in awful condition) for $30. The depth was the exact width of my oven rack. It was meant to be. I plasma cut off a 40lb oven rack sized piece from the end without the drain, cleaned it up (there was much grinding and acid soaking), seasoned it in my grill, and now it lives permanently in my upper oven. Yeah, it takes almost an extra half hour to properly pre-heat my upper oven now, but it's worth it.
The bigger remaining piece became a fireback for my fireplace.