2. You have a doc, but he's booked for two weeks or more. Problem isn't an emergency but it would be if it was left for 2-3 weeks.
3. You don't have a doc, and can't find one to take you in the next two months.
4. It turns out only to be an ear infection, but the baby hasn't stopped screaming since 8pm and it's now 2am.
I'm sure there's more, shall I go on.