You can, but most dealers tell you to put something between the cookware and the stove (like a scrap piece of soapstone, which they can often get) because the stone will stain if it is spilled on. Which I never understood because you can get sinks and counter tops of soapstone, but maybe those have different compositions.
The heat output isn't really affected by the material choice (that's all efficiency and size dependent), just the timing. Like I said with soapstone, you get less in the beginning because of the time it takes to heat up the mass in the soapstone (typically that's called thermal lag) but it holds heat longer than cast iron. It's not uncommon that I'll go to bed with the stove at 450 and find it at 250 in the morning. I do like the window as well.
Regardless of brand, I've seen more failures in steel stoves than cast or stone. I don't know that reliable steel stoves don't exist but I looked only at cast iron and soapstone when I bought last year.