Maybe if people have the option to delete their very last post and no others this could be a semi-god idea (in instances of accidental double posting, posting in the wrong thread and so on). But as people have already said you can just edit your posts anyway, and if it really needs to be completely removed you could just report it.
Im not too keen on this idea though personally, because on several occasions I have seen people throw a tantrum and start editing all their posts to blank. That is bad enough but at least you can see that at some point the post existed, and you can see when it was edited. And also it could prove to be extremely disruptive and confusing if posts just started to get randomly deleted by people for their own spurious reasons.
I don't know, I can just see this being easily abused if people had the option to do it.