That’s a good point, and obvious now you point it out.

On the other hand, when water turns into steam at standard atmospheric pressure, it expands in volume by about 1,700 times.

Whereas the gas in your stove is already a vapour, mostly methane, turning in to mostly water vapour and carbon dioxide. So the expansion ratio isn’t going to be anywhere near as high as that.

I’d say you’re still right.

Still, I wonder to what extent an exhaust fan does help.

If the exhaust fan can vent x cubic feet per minute and the room is y cubic feet in volume then it takes z minutes to full ventilate the room, etc etc.