I'll say this- a player who doesn't use his aspects isn't really playing fate... the thing I fell in love with about fate was the fact that your actual character- your persona and not just your stats- make it onto your character sheet in a meaningful way... that story affects mechanics as much, in fact, more than the other way around.
That, and the statement about him spending time trying to talk other players into setting up aspects for him to tag... costs them their FP or turns to do, and benefits him. Sounds like he's trying to relegate them to support staff, and that's also not OK. If every combat works out to them feeding him tags, then it gets boring fast- all of the sudden, it's not a game your other players need to show up to- it's this guy's show.
So talk to your other players, and make sure they don't let him force them into support roles- make sure they know they don't have to do what he asks when they could just as easily shine on their own. Teamwork is great, but it needs to go both ways to really work. Let them know they don't have to play along with him if they don't want to, they can take the free tags if it benefits them, and they can handle your conflicts without resorting to his chosen strategy. IE... let him hang in the breeze a bit, without free tags, and see if he starts spending him. If he does, problem solved, move on.
4-5 FP isn't bad by any means, unless the only reason it's that few is because you haven't been compelling him as often as the other players (which means you aren't using his aspects, see point 1). Other things make him sound like a hoarder, the number doesn't. Compel him more or less as much as you do them, and see how bad it gets.
If he starts stacking up to double-digits... and he's still not spending, then you have a serious problem, and one easily fixed. Keep doing what you're doing, and simply put a cap on how many FP's can be carried over from one session to the next (say, 5 or your refresh, whichever is more), on the premise that during down-times, your character ends up using them off-screen for other stuff (remember- these stories aren't their whole lives- just the highlights... Dresden has plenty of work... we only get told about the interesting Side Jobs and big case files). He may complain and tell you his character doesn't, but just tell him to deal.
This isn't unreasonable IMO (I'd certainly have a problem with one of my characters carrying 20 refresh from the end of one campaign to the next, when they're separated by half a year or more), and as a house rule that affects everyone, isn't strictly imbalanced. Once he figures out that if he doesn't spend them, he wastes them... he'll start spending them.