This is a great idea and in my mind one that will work, if handled correctly.
Lets take a look at Aussie V8 SuperCars, they have, in the name of parity, standardised aero, suspension, engine components, brake components, even the gen2 chassis are standardised. The cars weight and horsepower are all the same, yet many of the components are manufactured by Triple8 (Holden), and DJR (Ford) they also lease engines to other teams, the engines are exactly the same as the ones in their cars, they also prepare cars for some teams. Even the Nissans (Kelly Racing) have come to the front now after a few years of development and are consistently in the top10, Brad Jones racing is a small budget team compared to the above mentioned teams, but constantly "punch above their weight" all due to controlled components and regulations.
Triple8/Redbull were dominant for many years through the talents of Craig Lowndes, Jamie Whincup and now with Van Gisbergen, and it's only now that DJR/Penske have started to push them for poles & wins via Scott McLaughlan & Fabian Coulthard, and it's not due to the cars, it's due to the drivers. When a field of 28-30 cars has less than 1.5seconds between 1st and last it makes for very intense racing, not only for the butts in the stands, but for the teams and drivers.
Also lets not forget how well Volvo went in their debut season, if the parity regs weren't in place do you think they would of been as competitive?, definitely not.
If Liberty Media manage this correctly they can take F1 to new heights IMO, one of the problems with F1 is budgets, the difference between the haves and have not teams is massive, hence the have not's employ heavily financially backed payed drivers just to have the money to stay in the game, then they have to hand over massive amounts to lease noncompetitive engines from the top factory teams, while the top teams can employ talented drivers who get payed multi millions and have enormous budgets due to reaping millions in leasing Bspec engines.
Of course these ideas will ruffle some feathers, but more so Ferrari & Mercedes as there dominance will be threatened, hence neither team was willing to lease engines to RedBull when RB were at loggerheads with Renault, they knew that RB could potentially shake up their dominant position and win races. It will also diminish the financial benefits from hybrid engine leasing.
One of the biggest issues I see in F1's past is the manufacturers having an active role in the car regulations, this idea was never going to benefit all parties, and is one reason why F1 (Liberty Media) is taking the approach it is now, and I agree with it, no team or factory should have a controlling factor within the regulations in a sport it competes in. But this is what Bernie was best at, playing the teams, and he created the scenario we see today in F1. I just hope for the sake of F1 that Liberty can find the balance that will create fair competition, as the pinnacle of motorsports and it's future, is in their hands.
I realise some will disagree with the above, and it's fine to have your own opinion, but when you really look at it, component parity and controlled regs can have very positive outcomes for all parties.