In a word - no!
Blimey - could you imagine the drop down menu for how your NI is used & what benefits you'd get.... as per above, that's a high risk philosophy - hoping the paramedic can cure you, without needing to see a GP, Dentist, Doctor/Nurse at hospital etc at the time of need!!
You did used to be able to opt out of certain aspects of NI, but that related to SERPS, S2P etc - that's been abolished.
NI = National Insurance - this is mandatory based upon earning levels, it goes towards NHS, social security type benefits and the state pension. NI ceases at State Retirement age (currently) BUT the costs of covid-19 will almost certainly see changes to NI (increases in contributions) and increased taxation (in due course).
PS - You can even pay voluntary contributions to ensure you get the full state pension (a very undervalued benefit!!).
Please don't take this out of context, but you're an adult (I think with a disabled child? - apologies if wrong) and a teacher and if you don't know what NI is and what it's used for, then it's a pretty sad indictment of the 'financial' education that we provide for our children.
It may well be something that you just weren't interested in at school, but I have been suggesting for sometime (in chats with headmasters when delivering some some other coaching sessions) that the curriculum needs to factor in fiscal education - not just at secondary school level either.
I sent some ideas to a publisher a few years ago, about a series of books on this subject and they were very keen, but I just didn't see how this could pay my own household bills, if I gave it the time needed - as that would be at the detriment of the normal day job.