I think probably because no-one would ever say that.
To go deeper…
Let's say you saw seven separate people going about their own separate days in a park, you could say you saw "seven individuals" in the park.
Let's say you saw seven humans in what appeared to be a group but you wanted to emphasise their uniqueness, you could say you saw "seven persons".
Though "people" would always far more common in the those cases, there's a bit of "extraness" available if you want it.
Legally a company/corportion can be "a person", put seven companies/corporations couldn't be seven "people".
"Corpor" means "body" - so our human souls have been given bodies in the same way as a corporation has.
So this pretty much gets across the "individual self" or "unique soul" aspect of "person".
So, to conclude, it'd be possible but very weird to label the members of "a family" (ie. A single "body") as containing seven "persons" because the whole point of "a family" is that it has a one-ness to it.
It'd be like describing how many "drops of water" are in the sea. The whole point of "the sea" is the one-ness of it.
So that's a far more complicated answer than you might have expected. And it's also one with which many people could argue, I'm sure.
The typical answer would simply be, "we'd just never say that, 'persons' is mostly just used for legal things" but it amounts to the same thing. :)