Separate doors make it easier to access without releasing the chickens, if you need to (they're relatively habitual and if they never use the "people door" they won't really try to).

Easier to automate a small door, and control where it goes.

It looks cooler; people like "small doors for small things" - like the half-height garage doors at Walmart for shopping carts.

If small enough, it can reduce at least SOME predator incidents (but this is minor).