Personally, I have never liked the term, "Exonumia". Rulau's reasoning for inventing it was never explained to me, so I was left with the explanation, "exo = outside of, and numia = numismatics". To me the word implies that tokens, medals, and such were outside of the realm of Numismatics.
My belief is that there is much more Numismatics going on with medals and tokens than there is with coins. To my way of thinking, much of the research on the entire series of United States coins has been done and has been nicely summarized in the Guide Book of United States Coins.
Medals, and especially tokens (expressing my own selfish interests here), offer almost unlimited opportunity for ORIGINAL research which is what Numismatics is all about. A person who makes a living buying and selling slabbed (identified, graded, and authenticated) coins by looking up values in the gray sheet or by buying silver by weight and fineness then selling it to a refinery is not a Numismatist! Given almost any medal or token, answering the "Five Ws and one H" questions, Who, What, Where, When, Why, and How? will involve some serious research.
Some may feel a need for a word such as Exonumia, but for me, Numismatics is the word to use. Similarly, I don't think Neil Shafer's term, Exographia, has a use. If the paper item of interest is Numismatic, then it Numismatics is the word to use. If it is other than that, the well-accepted term, Ephemera, is appropriate.
I think research into official U.S. coinage is far from complete, as evidenced by the continual appearance of great articles in specialty publications and elsewhere But I do agree that much or the opportunity, challenge and fun lies in researching tokens, medals, and obsolete paper money. I do consider these very much mainstream numismatics, not outside of it at all, just outside the official government-issued branch.