If F1 is taken over by Americans, I would imagine that the series will marginalize the FIA as much as possible too.
That may be hard to do Jeri, The FIA owns the rights to F1 and FOM has a licence for something like a hundred years for the huge (at the time anyway) £300m that Bernie paid to get the commercial rights.
FIA was forced by the EU to split up the commercial and governance elements of F1, the Bernie deal was the result. This is why now the strategy group (again created in exchange for more income to the FIA) can only suggest & recommend changes to the rules, the WMSC still has to ratify any major changes the Strategy group puts up. The WMSC is an FIA body.
Now no one is going to invest $1b let alone the suggested $6b and then end up with just a breakaway series, because make no mistake the FIA F1 series would continue to run, with a different promoter if necessary, if the contracted commercial rights holder breaches the terms by ignoring or side stepping the FIA rules and regs making process.
Then what exactly is being purchased if not 'F1'?
The rights to all income from F1 until 2110. The FIA would have to prove breach of contract on the promoter's side to prevent that - and even if the income fell to, say, $100 m per year (about 1/10th of the current figure), it still would represent a profit. And after the initial purchase, the buyer need not lift a finger for this to happen, as F1 tends to produce at least some income even at its most ridiculous. Oh, and you have quite the dinner table ornament to show off to your wealthy friends... "Oh, you have a nice skyscraper complex. Do you have the income from one of the big symbols of Western capitalism?"
It would be the ultimate in passive income... ...if that was what Qatar wanted.