Should some of its capabilities/duties be ceded to or shared with other Services?
The present situation is afaik that

- the USAF doesn't have good own EW/SEAD assets for penetration of enemy airspace since they gave up the F-4G/F-16C combo wild weasels. They relied instead for years on USN assets (Growlers in the near future) and on the use of AGM-88 (and its modifications) by fighter-bombers.

- the USN doesn't have a good midair refueling capacity for long range missions and relies on USAF KC's. The USN is afaik even retiring dedicated refueling aircraft and will depend on KCs and buddy/buddy refueling in the future.

- the USN doesn't have a good carrier-based ASW/MPA capability any more and will need to co-operate with P-8's for long-range ASW/MPA in a few years.

- USAF / USN / USMC share the fighter-bomber mission, even when enough land bases are available.

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Imagine a blank sheet. There was no Cold War. The U.S. forces were not particularly large but developed the same equipment. The U.S. government does not seek conflicts nor does it promote them.
The idea to justify defense expenditures with alliance obligations fr Asian allies is widely being considered ridiculous as long as these allies spend less % GDP on deterrence than the USA does. Have a look at the inventories of other wealthy nations. And at potential adversaries' inventories. Remember the air power capabilities of the allies.

Now think about realistic air power requirements.

I think a fleet of 500 Super Hornets/Growlers, a hundred C-17's, a bit more than a hundred large specialty planes and two large CVs would be considered as a normal and appropriate air power inventory (till 2025) in this case.

The world isn't that sane, of course.