It’s been repeatedly documented that people rate composite faces as more attractive than the faces used to create them. The “beauty is average!” conclusion is just lazy analysis, and I haven’t really seen other theories to explain this, so I will posit one.
Composite “average” faces will essentially blend out features that are very feminine or very masculine. The resulting composite face is attractive to mates because it could conceivably parent an attractive child of either gender. An evolutionary hedging of bets, if you will, that increases the chance of their offspring being successful on the sexual market. I am dubbing this measure of beauty the Dimorphic Attractiveness Quotient. Its possible attractive faces simply have a high DAQ.
Think about a guy like Pat Tillman, a lantern-jawed alpha male (RIP). If he had fathered a son, the child would no doubt be a masculine wonder. But imagine if a daughter accidentally got his jaw? Yikes. If he had a daughter with a feminine looking woman, it could help bridge the gap, but the biological daughter of, say, Leonardo DiCaprio, would have no such handicap. And Pat Tillman isn’t the best example here, his jaw is just the single most masculine feature I could think of but the rest of his face would be pretty high in DAQ. A better example of an extreme masculine face is Andre the Giant. Yeah, Andre makes the point much better. He’s also pretty symmetrical by the way, the symmetry = beauty theory never made any sense outside of cases of deformity.
It works for women, as well: A delicate flower of feminine neoteny would most likely mother a pleasant looking daughter, but a weak son unable to compete for resources or mates.
This isn’t to say very masculine or very feminine faces are de facto unattractive. It is merely that evolutionarily speaking, those faces are a gamble. Sometimes, those gambles fail:

Sexual dimorphism is a beautiful thing but it must toe a delicate balance.
I have a friend who is a dead ringer for Fred Flintstone with a chin the size of Texas and he’s dating a tiny, mousey cute Greek/English girl. I’m rooting for them to have kids just to see what comes out.
(Please note that I wrote this post in twenty minutes pre-gym while waiting for my creatine to fully absorb with one hand on my big balls, yet it still contains more original thought than most federally-subsidized grad students can muster in 6 years. I believe the term of art here is “suck it”.)