Remember, R-O-N* spells D.A.N.G.E.R.
(* Resume Own Navigation, for the pilots)
That's what I was taught anyway.
The reason we use headings is because that is what is required to ensure standard radar separation. I'm sure most controllers have had their fingers burnt by routing an aircraft 'direct' to somewhere, only to have it point to a position 10 miles north. I know I have.