Gas stoves exhaust right into the house. Besides raising the CO2 level, they produce CO, carbon monoxide, and smoke from whatever impurities come with the gas, that vary according to where it comes from. I doubt anybody bothers to get the radon out. That would cost money.
Propane is probably purer than straight-up NG, but it's exhaust is still exhaust.
radon decays into dust in a couple of days, but natural gas deposits are tens of millions of years old and have been out of touch with potential radon-generating rocks for weeks or months by the time they reach your stove burner
In a week or three, anyway. Anywhere somebody has bothered to liquify the NG, the radon will have decayed before it gets vaporized again. Where pipelines lead straight to gas wells, the dwell time in the pipeline before it is burnt could be quite short. But there might be negligible radon even at the wellhead, as it would need to be picked up from surrounding rock on the way out, unlike e.g. helium which accumulates.
Probably other toxins are more important: mercury vapor and hydrogen sulfide are usually mentioned. Hydrocarbons other than methane may burn to carbon monoxide or soot. Gas is said to get much less processing before delivery than it used to.
SpaceX will probably purify theirs before pumping it aboard, just to increase the useful life of their Raptor engines.
My home as a kid did. I don't know why it's fallen out of favor, since I can't imagine it costing more than $100 or so in parts and labor on a build... If we can have a bathroom vent, why not a cooking vent?
If the vent moves more than a certain amount of CFM air, then an exchange system is required, but that takes almost a restaurant grade vent to get to.
Propane is probably purer than straight-up NG, but it's exhaust is still exhaust.