They do have an airforce, they have Vertibirds and they had a number of them at the Long 15.
As for naval/coast guard, it would have been great to see some Vietnam or World War 2 era type PT Boats going up the River or in Lake Mead.
But as to why we don't see those things in the Mojave. My guess would bureaucracy, politics and above all cost. The NCR isn't there for full scale war, it's more of a defensive police action.
I was always bothered by the fact that Bear Force One seemed like it was supposed to protect itself.
You know, it's not like the president of the NCR is important enough to warrant two or three vertibirds. He's just a president after all.
Vertibirds being taken out with small arms fire was a bad game mechanic Bethesda came up with. I never tried to shoot down Bear Force One but if it can also be take be out with small arms fire then that's just stupid. They are military aircraft designed by the Enclave and yet anyone can shoot it down with an assault rifle?
If we set aside "the play must feel like Rambo on super steroids" aspect. Vertibirds must be able to take some serious damage in order to be shot down and I don't see the Legion or anyone else with anti-aircraft weapons.
We also have to look at the area we saw the Bear Force One. It was at Hoover Dam. A place full of Rangers, Heavy Armour NCR and the place was checked before it even landed. The threat wasn't so much it being shot down by AA but sabotage and assassination.
I don't think Vertibird being shot down by small arms fire was a mistake, simply a game play mechanic to make the player feel awesome. http://www.youtube.com/watch?v=v7ssUivM-eM Same reason we can take out busses with a pistol.
By the time of New Vegas, I believe the NCR didn't feel the BoS were a threat and really they aren't. Even if you get them to leave their hole they don't go out and attack the NCR. In the endings I think they do, but no in the actual game.