Consider it a self-compel
Although concession does give you greater control over your fate, you're still losing--and you're choosing to lose when you still have a chance of winning.
you can interrupt any action at any time before the roll is made to declare that you concede the conflict. (Fate Core 167)
That means if the dice are rolled and you're taken out, you can't call backsies. If you're not taken out yet, it's possible to still win.
By conceding, you're forfeiting the chance to win, and that's pretty much a self-compel. And you get extra points for the consequences you got in the conflict as if each one had been compelled, because "[y]ou can think of this as a compel of each aspect taken in the conflict[....] [T]he assumption is that those consequences directly contributed to the character’s defeat." (DFRPG Your Story 206)
Consider it a drama bribe
The idea driving Fate storytelling is that every time something happens to complicate your life, you get game currency which you can spend to make your life easier later. Fate Core is very up-front about the fact that the Fate point economy drives this cycle of crisis and victory.
Conceding is still losing, and you should always negotiate a concession until it has a dramatic bite to it, like any other compel. Concession Fate points are a way of encouraging crisis while simultaneously providing the tools for future victory--again, just like any other compel or invocation. It's the way the engine powers the story.
It means your villain can usually escape to plot another day
NPCs can concede too! And should, often, if they're smart and have a sense of self-preservation. It gives the players a sense of accomplishment (because they achieved whatever goal they had when they entered the conflict) but sets up the villain as canny and positioned to wreak more havoc because of his fistful of Fate points.
Consider it an opportunity for the GM to do less work
Hey, my player's gonna tell me how he gets shafted instead of my having to come up with it. Awesome. I'll throw him a couple FP in appreciation.
Why do you want to discourage concession?
Concession is a pretty shiny mechanic, and although Fate is very flexible about many things, discouraging players from being able to cash in their cards when they walked into too much trouble is going to make them more cautious than the "proactive, dramatic, competent" characters Fate wants to tell stories about.
Allowing concessions is a frontline weapon in the war against ten-foot pole paranoia and the boring, time-wasting practices that come with such paranoia.
Come on into chat when you have the rep and we'll talk about what your underlying goals and motives are for discouraging concession. Probably we can work out some other way to satisfy your motives.