Let's say I decide I've had enough with this whole Federation business and that humanity would be better represented by a Starfleet that follows my particular ideology. Assuming I could get enough people for crew and support, why can't I start my own Starfleet?
I could replicate ship parts until I have a couple vessels. Go to new worlds and present myself as the official first contact of humanity. I could fly to Vulcan or Bajor and tell them no actually my organization represents humanity.
What's going to stop me?
Could I replicate charged batteries, then plug them in? Or would it take more energy to make the battery than you could get out of it? After all a battery is just a chemical reaction.
Of course you could. The process will take more energy than replicating a drained battery too.