So the litter acts as a trapping agent by desiccating the waste. Only occasionally (usually when we're lazy about cleaning) does the litter stink.
The smells the cat cares about are its pheromones/scent. Cats are highly smell-oriented (they don't taste food as much as smell it), so venting all that cat-smell outside could cause the cat to find other places to mark.
I get what you're saying, but IME cats are more likely to start hunting for shoebins and handbags to pee in when the litter box is too dirty...not when it smells too fresh. They're pretty anal about keeping clean.
In any case, there is more at stake here than scent-- do mind that the ammonia vapors from cat urine are toxic and can lead to hard-to-diagnose respiratory and psychological issues. A dirty litter box will also breed toxoplasmosis spores (dessication actually makes this issue worse-- dry spores are more easily spread when disturbed).
You really don't want standing organic waste in your home if you can avoid it. It doesn't benefit you or your cat.
The smells the cat cares about are its pheromones/scent. Cats are highly smell-oriented (they don't taste food as much as smell it), so venting all that cat-smell outside could cause the cat to find other places to mark.