When is there a need for a special branch of military? When there is a need for special equipment? When the battlefield in question is important?
The US Army does just fine operating aircraft and ships. Yet separate organizations, the USAF and the USN, do exist for airborne and seaborne battle, respectively. That's because those types of battle are crucially important and technologically uniquely demanding as of today.
However, there is no separate organization for swamp warfare, which also requires very special technology but is not quite as important as a standalone battlefield. Nor are there separate organizations for jungle or desert fighting, even if many key wars will probably be fought in those environs, because the environs don't require special technologies to the extent air warfare or undersea warfare does. There is an organization for amphibious warfare in the United States, but it's considered lesser than the Army, Navy and Air Force.
One might equate the seas of the Federation worlds with these lesser battlefields that either don't mean squat or don't require special technologies. One might do the same with the dry surfaces of said planets, and decide that there is no separate Army in the Federation, merely a minor branch of Starfleet.
In contrast, one might postulate that the Federation would need major organizations on par with Starfleet to deal with certain special environs - say, there could be a completely separate fighting/exploring force for areas of space where warp travel is impossible, because starships and their crews would be as useless there as submarines and their crews are on dry land today.
Onscreen references on the matter seem simple enough, though. No other organization seems to rival Starfleet in military matters, whether these involve warp-speed battles or ground fights. Even police work seems to be conducted by Starfleet in a highly centralized, all-federal manner. Against this, it would be a bit odd to consider Federation Naval Patrol an organization that rivals Starfleet or is the sovereign armed force of the seas or so forth. All the more so when this sounds like a civilian organization, with "Federation" so prominently in its name.
Let's also remember that Tom Paris wanted to enlist there at a young age. Perhaps the FNP is like Boy Scouts - an organization for children? There would be plenty to see and learn on and in the seas, and the open and/or three-dimensional environment could also serve as a lead-in to the space travel that adults do.
Timo Saloniemi