It's not a question of a unified command, it's a question of drastically different missions and requirements. Our Navy does things with their jets no one else in the WORLD does, and that carries certain material requirements. Same can be said for the Marines, and the Air Force.
In Ack-Ack's linked article Lt. Gen. Chris Bogdan explains how the 70% commonality goal was attainable, but that:
"Man, is [compromise] a hard thing to do when you’re spending billions of dollars,” he said. “You want what you want, [but] hopefully get what you need."
And:
"If Pentagon leaders do choose to build a multi-variant plane to serve multiple sets of requirements, he said, the services will have to embrace compromise to a greater degree than happened in the $400 billion F-35 program."
Clearly that would be easier with a unified command (at least on the procurement side) that can cut through the bullcrap and keep all the services in line. To say that the USAF's needs are so different from those of the USN that they need a completely different fighter is absurd. That's like saying the Canadians, Finns, Aussies, Swiss, Kuwaiti, Malayans, and Spaniards can't use the F-18C as an air force jet. Their air forces all do, and chose it over the likes of the F-16.
I mean really, the Swiss! They don't even have a coastline!
You have to love those German MiG's... A DACT goldmine. (Btw. that is just a promotional video for some Swiss air show.)