Niall,
I fully understand that on any individual design it may be possible to create more variety with one combo of holes over another. That said, in theory, if ll things being equal - like designing in a cornfield rather than a spectacular site that give more design cues - that the pure numbers by virtue of playing 10+ of them vs 2-4 par fives suggests it would be easier to create variety with 4 par 5's and 10 vs 11 par 4 holes.
I can easily think of 4 very different par 5 holes in concept. And, I can think of way more than even 12 par 4 concepts, but feel they tend to run together a bit no matter what you do in that cornfield.
I also believe that for the most part, par 3 and par 5 holes were introduced solely to provide variety from par 4's. Par 3's have no shot related strategy and par 5's may have strategy, but it can be created in two shots, and the third was a bit unnecessary. I just imagine some old Scottish bloke looked around, got tired of similar holes and got an idea for 3 and 5's, maybe even 6,7 and 8 par holes, which was given the thumbs down......