On the upside, it encourages you to diversify things. Keeps all your characters from acting like you if you, say, assign each one a different Olympian as a source of traits. Allows thematic implications to be developed.
On the downside, it can produce excessively tidy results that shoehorn the plot into an obvious formula. Slytherin as temperance is more plausible than justice, but it's still a weak fit. And as I was considering whether to stick each of seven characters with a deadly sin as a flaw, it occurred to me that would mean sticking one of them with gluttony, which would require a plot too comic for other elements.
And there are other ones. I knew one of the seven had a widower father; a second one was being raised by his (male) guardian; a third had a significant father, or so the first impressions said. And I started to introduce a scene with the point of view of a fourth, and her father was talking and I went -- wait, is this seven all being raised by lone men?
Now, if I were doing it schematically -- hmm, not too tidy. For four, it would of course be raised by both parents, by mother, by father, and orphaned. To plump out to seven, perhaps, raised by a male guardian and by a female guardian, and -- umm -- raised by an enormous extended family.
Too many characters for me, and I don't need it so neat. Just throw in a few exceptions. Though, of course, it can work. Order of Stick managed to give most of the main characters issues with their fathers rather than their mothers, and it worked. (One notes that Burlew sort of slipped into it, not realizing until after that it was all daddy issues.) But not here, I think.
Now I just have to start figuring out some parental occupations so they aren't all the same there, too.