Kitchen gas stoves unsafe?

The amount that they burn supposedly is not enough to mess one up, but. Many states like mine have put into code, gas oven in new or retrofit, need an exhaust fan also. Back in the 50's one of the selling points for gas stoves was supplemental or emergency heat. That went away as people did get nailed by them. The the talking point of they do not burn enough to make an impact in the scheme of things cam into play. Only in tighter modern construction, they do.Which has lead to codes like my state put in, the required ventilation fan.

Gas stoves rarely put out any measurable carbon monoxide and they're only using a small fraction of the gas burned in a water heater, which also does not NORMALLY put out much CO. An improperly operating gas heater can generate 5000 ppm of CO, which is why it has to be properly vented outside.

the pilot light is a safety precaution "Do Not Touch" 

Gas stoves rarely put out any measurable carbon monoxide and they're only using a small fraction of the gas burned in a water heater, which also do not NORMALLY put out much CO.  An improperly operating gas heater can generate 5000 ppm of CO, which is why it has to be properly vented outside.  Maybe you're thinking of carbon DIOXIDE, which is a byproduct of burning propane or methane gas?

providing the burners are properly adjusted the product of combustion is carbon dioxide NOT carbon monoxide 

CO is a product of incomplete combustion. It isn't necessarily generated by an open flame.

Regardless of which, you don't cook when asleep, so wouldn't succumb to hypoxia without noticing

Anytime something is burned, water vapor and carbon monoxide is generated.

FALSE. CO is a byproduct of INCOMPLETE combustion. Complete combustion generates carbon DIOXIDE, not CO.

The general idea is that most people will have a door or window ajar when cooking, if only to vent the steam. This is sufficient to vent any fumes as well.  A lot of people will also have an extractor fan in the kitchen.  Plus the oven etc. is not running for hours unattended, unlike a boiler, and you'd know if it wasn't burning properly by the look of the flames.

I asked my local Columbia Gas Company official that question. I was told that most homes have enough ways for oxygen to get inside and provide safety for stoves and ovens. At one time, my gas furnace failed, and in the meantime, the furnace repairman told me it was safe to turn on all my stove top burners BUT I should open a window just enough to place a pencil in the gap. This provided enough oxygen to provide for safe combustion of the burners and I suffered no ill effects. 

Open a window and maybe run a fan for ventilation while you cook and install a carbon monoxide detector