Who cares about stains on baking sheets. I never have. 

Flat, thinsheets of stainless are terrible when exposed to heat. They will always warp more than most other metals. This can be controlled a bit through design, but, you need thickness and geometry to not cause obvious warping. (It will warp, you just don't notice it with something like a large pan with a thick base and swoopy sides.)  

 I’m concerned stains mean they’re not getting fully clean. 
I don’t really mind a thick baking sheet as long as it stays flat. It’s probably an asset, really. 

 Do you worry about seasoning on cast iron? If not... I suggest not caring about stains on enamel steel. 

I... Could make you some stainless baking sheets that would not likely warp, but... They would be expensive since the material would have to be chonky. This would also have a significant effect on the baking time as they would be a heat sink.  

 As far as I know, seasoning on a cast iron is polymerized fats only, from an intentional application. Other food residues (are supposed to 👀) wash away. Having actual food residue seems like a health hazard, as well as affecting the flavor of your next dish. 

 I'd take some discoloration vs. Any nonstick poison coating on a conventional modern baking sheet. You could also use parchment paper or silicone baking sheets (if you trust the silicone) to prevent stains on the pans. 

I tend to not care too much about stains on the enamel. But if you do, the only way to solve this issue is to spend a lot of money. 😅  

 I avoid nonstick coating like the plague, don’t worry!