I have seen some systems where there is like a 5 minute grace period, and in that time you able to delete it.
My feeling is that you want to delete a post because you made a mistake in it, and it's easier to start again than to edit it, or in the heat of the moment you wrote something that you regret. Either way, I'm not sure what benefit there would be of having to earn the privilege. All you do is embarrass people by leaving them with a public post that they regret.
If you want a reward approach, then maybe apply it the the ability to give Kudos to a post?