Well the reason in not allowing it is to stop people from abusing it's use. Same as why not every member can access the admin panel obviously. Not everyone can be trusted to use the functions correctly.
Elites and staff can delete their own posts, other can't (although you probably know that) and I don't see a reason why it's needed. If you make a mistake thats fine, if it's a big deal, which it usually isn't, it will be removed. If not, it's not a problem.