ST ENT showed that the native armed forces still exist. Reed joined Starfleet instead of the Royal Navy.
OTOH, all we really know is that his dad would have wanted him to continue the family tradition of serving on top of lots of water. This does not mean the Royal Navy should have continued to exist - after all, Reed did not join such an organization. And the reason he quoted was the fear of water, which would keep him off the United Earth Seagoing Service, too.
Also, the RN existed during the past two generations of Reeds. AD 2150 could easily have marked the end of that organization, and all other national ones, without affecting the setup here one iota: Reed would already have made his choice back when the RN was a thing.
It has never been stated or implied that nations states stopped existing under a one world earth government (perhaps similar to the present day E.U).
And the opposite was never stated, either. But significantly, we see the UE government in action in ENT, while we never see national governments in any sort of action post 2150.
Earth would have its own defense force for the planet, Starfleet operates in space.
Sounds awfully artificial. Today, the Army has ships, the Air Force has armored surface vehicles, and the Navy has aircraft, exactly because geography matters very little in modern warfare.
Also, how to define "Earth"? Does it include the Moon or not? Mars or not? Earth Colony Two or not? If "Earth" is defended by interplanetary or interstellar means, then one might just as well skip that shit and hop directly to defending the Federation.
Doesn't mean there wouldn't be Starfleet people whose exclusive job it is to stay on Earth and defend that planet's surface. This just doesn't call for a separate command hierarchy, and indeed would suffer from having one.
Timo Saloniemi