Are you talking in general or navyflier's case? Generally, I agree, it doesn't make sense, but w/ his example the LOA apparently does exist, so it's kind of academic. Or maybe that was your point.
I guess in xnvyflyr's case...
If I am creating an LOA, I can't create authority, I can only share or delegate authority that already exists. If authority could be created, then govt agencies could get together and expand their powers. Obviously, some do, but in this case it could/should easily get shot down if it wasn't approved by atleast big FAA.