aka it seems fair to me: part of maternity leave is about coping with very late pregnancy and physical recovery from the birth. The father can never do that part, so is only needed to provide a parent at home for the baby. If the mother is already doing that then generally there isn't much of a case for the father to do it.
I wasn't employed when pregnant, I didn't get maternity pay, so yes getting any pay for a parent being at home is dependent on the mother working. It also meant DH couldn't take this leave, but we couldn't have afforded the only earning adult in the family to drop to SMP anyway.
Looking at who is eligible for it:
Scenario 1: Both work
Can choose who will stay at home and receive SMP from 2 weeks post-birth up to 50 weeks, changing at any point.
Scenario 2: Father works, mother doesn't
Father gets first two weeks of paternity pay, no-one gets any SMP.
Scenario 3: Mother works, father doesn't
Mother can have SMP until she chooses to return to work (for up to a year). But she is sole breadwinner so is unlikely to be able to stay off all that long (as SMP drops as time goes on).
The aim is that parents can choose who stays at home to care for a young baby whilst also enabling physical recovery of the mother. The government will only pay this for parents who are in employment during the pregnancy, having a SAHP is not funded by the government. This sucks for those of us who did not choose to not work but who have a household income too high for means-tested benefits, but there are people far worse off.