Back to the original question posed on this thread, no, I don't think a quad should be *mandatory/required*. However, I definitely feel a quad should get by far the highest points out there, and even moreso if used in combination. The same goes for the ladies as regards a triple axel.
One only need to look at this most recent Olympics to see that the quad for men is thee hardest element/jump out there, only 3 men managed to land clean ones out of all the attempts. And, lol, the 3axel for the women is even more rare, Mao Asada was the only woman to attempt & land one.
If the quad was so easy for the men, or the triple axel so easy for the women, we would have loooooooong ago seen skaters landing them left & right. And that's just NOT the case. Many many many have attempted to do so over the years/decades, but only a handful of exceptionally gifted athletes have ever managed to land them on a consistent basis (i.e. a quad for the men, and a triple axel for the women).
Case in point:
Men that have landed the quad on a consistent routine basis -- Stojko, Yagudin, Plushenko, Goebel, Lambiel, Joubert (6).
Women that have landed the 3A on a consistent routine basis -- Harding, Ito, Asada (3).
I rest my case.