Yeah, there's no comparing a pizza cooked on a tray to a pizza cooked on a proper stone.
I'm imagining a pizza that's charred in the middle and soft out the outside.
I'm also imagining a more realistic scenario where there's a small but noticeable difference, and wondering what it's like to be bothered by that. I can barely smell things at all, and my taste buds are weak, so I appreciate texture a lot... And I still can barely understand the problem. Maybe I just enjoy variety of texture because I'm weak in other culinary senses.
Like how I sometimes make random foods spicy on a whim for sake of variety, or I char foods because the black carbon tastes different. Except that's not unusual, people enjoy toast... I just go a little farther
There's a couple points in favor of stones:
1. Because you preheat stones (but not pans) they cook the crust faster, which means that you'll never get a soggy crust from the ingredients soaking through before it's fully cooked.
2. Stones tend to absorb moisture, meaning that the crust will be crisp and just a little chewy, rather than a doughy mess (if you deliberately make pizza crust thick and doughy, you sacrifice your right to talk about pizza).
3. It cooks the pizza much more evenly throughout.
4. You can free-form the shape of the pizza if you make your own.
5. Easiest thing in the world to clean. Just let cool and wipe clean.
The only real downside is that you can break a stone if you've got butterfingers. There's people dedicated enough to make their own dough for high-heat cooking so they can pop the pizza onto the stone at >500 degrees and get it done well in a flash, but that's rather more effort than most people would expend, so no pro there.