To adress this specific question for Paris, they put an upper limit on your income to rent specific housing with lower rent.
I'll scale down your caricature of an example though, the offers you can see are usually 15% to 20% under market price, not 75% like you seem to imply.
Not exactly sure what is your point otherwise, the difference in terms of giving someone an apartment with a lower market rent vs. giving that money outright will eventually lead to the same thing, except that the former is also a way to curb the very high rent inflation (among other things), and results in both cases in a significant increase in purchasing power, at a given income.
> If we realized that with a system like this we're giving 1 out of 1k eligible people the equivalent of a 30k a year transfer
This is not equivalent because giving someone that money doesn't mean they'll chose to live inside Paris, and this is a measure that goes beyond financial support. It's also a city policy aimed at achieving a specific population distribution.