With beauty being in the eye of the beholder I'm sure you are right, all plants can be considered ornamental -but not all have economic or "functional" uses. The boundaries often overlap - a beautiful flowering shrub has aesthetic merit but could also be providing shelter or stock-proofing as a hedge.
Actually there is a much simpler definition:
I buy it = functional
Wife buys it = ornamental
It's an intereseting question. I agree that all plants can be considered ornamental, by someone or other. As Fred says, it's a very subjective thing. And plants we now think of as having no value beyond being attractive may be found to have useful properties in the future.
But Clive's definition brought the first smile of the day to my face this morning