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.
You’d sure notice if the air in your kitchen was swooshing around at 671 miles per hour.
I suspect a sufficient ventilation would require something more like a lab fume hood that can pull a negative pressure on the area around the stove.
And from what I have seen, a good number of exhaust fans are straight up fake and just ventilate back in to the room rather than ducted outside.
Culinary Cargo Cult.