Somewhere I read that you should use a round mallet to hit a square chisel and a square (I assume this means flat-faced) mallet to hit round chisels because otherwise when you strike the chisel you could hit it at an awkward angle and cause it to mess up the cut. Is this statement referencing the top (the face that you strike with the mallet) or the sides of the handle? Is there any objective evidence that it matters what kind of mallet you use?
Despite my comment above, I feel this is a very valuable question:
Is there any objective evidence that it matters what kind of mallet you use?
I think you could find it, if you would accept anecdotal evidence, but I'm certain it would be contradictory. From everything I've read, going back to historical books and right up to modern Internet sources, and from what I've seen in various craftwork cultures (from Asia to Europe to the Americas) I think that what works best is primarily going to be a matter of individual preference. How each person arrived at those preferences is usually a melange of early experience based on what they were taught firsthand or read in a book, and then some amount of personal experimentation. This is the way it is for almost all handwork practice.
One thing is certain: what one person firmly says can't or shouldn't be used to drive chisels (be it a large steel-headed hammer or a rubber mallet or a deadblow) another person uses preferentially.