Traditional naval combat was basically replaced by arial combat during WW2. In those days (and maybe even today, I'm no expert) the limited flight range of planes made it necessary to have aircraft carriers for delivering air power, but the various naval guns, smaller ships like destroyers, and submarines were all ultimately there to either protect carriers from planes or, in the submarine case, to sink an enemy carrier and therefore also destroy their arial fleet. If you just give your planes a very long flight range then you circumvent the need for the fleet entirely. Since this is a Sci-Fi setting, you could even give the planes a more-or-less indefinite flight range by having them be solar powered or wirelessly recharged from ground based power plants.
Also, stealth planes are a thing. So are, in principle, are satellites with weapons attached. Those could be options if you want to have an "attack from out of nowhere" type capability.
Edit: As far as I can tell, the OP is looking to give up combat vessels. They could still keep cargo vessels. 527
Who's going to protect those cargo vessels? Well, the arial fleet can do that. That said, even if the OP does want to give up cargo vessels as well, I don't think that'd be hard to justify. As a general rule, they are fairly easy targets and it may well be worth taking the supply chain hit to just supply troops by air-lift. It's not like that's never been done before and, again, if flight-range isn't an issue then I don't see any reason this couldn't become the new standard.
Further Edit: It seems like some answers are basically saying that this can't be done because ships are needed to move materials. If naval power can't keep up with air power, then cargo and combat ships alike will be sitting ducks to air-power, especially if, again, the aircraft can stalk the seas without concern for flight distance. If the flight-range problem is solved and Navies can't defend against air attacks then it doesn't matter how much you "need" your cargo ships, they aren't an option. In short, it doesn't matter whether the logistics side of thing is worse in an air-only world. 527