Parmandur
Book-Friend, he/him
But why higher? That's my point. Why not use a generation method that doesn't swing so badly?
Except it doesn't really swing. It goes from maybe a hair below point buy to well above, to the point where a given character is effectively one level higher.
4d4 would give you a perfectly acceptable spread. I'd bet dollars to donuts that random generation people would hate it. You can't get an 18 that way. And that seems to be the point of random generation. Get those 35 point buy value characters on the table with a nice patina of legitimacy.
Random is fun, and makes for situations that would not necessarily arise from imagination alone. Personally, I love Traveler character generation the best of any I have seen, and dislike all point buy systems. The random factor creates an interesting dynamic for role playing, and even all 18's isn't useful if you keep whiffing the rolls in game.
Also love the random elements to Backgrounds in 5E, giving depth to a PC with a few dice rolls.