Unless things have changed, booze is sold under the Class 6 classification and not under the BX/PX Exchange. So alcohol purchases are only allowed for anyone with military affiliation (active, retired, dependent, reserve) or civilians on orders while overseas.
Exchange privileges for DoD and non-DoD civilians overseas is a good thing as long as the privilege is not abused and goods are not resold to locals.
Inside the US, DoD civilians really have no need for exchange access. It might be a convenience to shop at an exchange while working on-base, but it's not a necessity.
The Exchanges run other services, too, like the gas stations, auto repair shops, food concessions, laundry, and so on. These services are to benefit military members. If DoD civilians start adding to the demand, would these places be able to handle the increase without spending more to add store space, employees, stock, etc?
If a DoD civilian needs to have access to the exchange, orders can be draw up case-by-case. Showing those orders at the exchange will be all that's needed. Opening up the system to half a million more people across the nation seems like a fix for no real problem.