Yes, it does "cover" other stuff, and gaps in your NI payments can leave you not getting that other stuff. That's why you're allowed to top up your NI payments.
EDIT: Also, while it's true about health insurance (if you go private you have to pay both) it's not true for pensions. You get a reduced rate of NI if you opt out of the national pension scheme and opt in to a recognised provider.
Yes, it does "cover" other stuff, and gaps in your NI payments can leave you not getting that other stuff. That's why you're allowed to top up your NI payments.
EDIT: Also, while it's true about health insurance (if you go private you have to pay both) it's not true for pensions. You get a reduced rate of NI if you opt out of the national pension scheme and opt in to a recognised provider.