It wasn't done years ago because it is unworkable.
They could look towards MotoGP. Factories now produce a slightly lower spec bike (Honda's Production Racer is only different to the works bike in respect of the ECU and the valves), but these "Open" class bikes get other advantages = more fuel, more engines, softer tyres. You can buy a HRC bike and have it updated for two seasons for EUR 1.3m. Peanuts.
In F1, adopt the privateer concept. Marussia buys chassis from McLaren, pops an engine in and goes racing. They use their R&D budget to do this so it is not wasted developing a shit car and the big teams get some money back on their much better R&D.
Do that, and we'll be back to pre-qualifying within 3 years.