And it has the same problem as every other current solution.
Yes coops can keep prices from rising over time, but they do nothing to make units affordable up front.
Where the fuck are you going to get the capital to build/buy enough units to make it do anything?
The entire government budget looks tiny compared to the current value of the real estate market. The government couldn't even realistically fund building or purchasing 1-2% of the units in the country as coops, let alone enough units to make a difference in the market.
There are other better policies.