Yeah maybe it's not life or death, however there are a lot of cases where it is needed if a parent wants the best for their kid(s).
Scenario 1.
Extremely bright kid, sits in class and does all of the work they are given at Primary School. Teachers have no time for them, they always say they wish they could spend all day with kids like it but they just can't as their time is taken up by kids who are just little pricks (Im not talking kids with actual conditions or special needs, just ones where the parents think the school is just a babysitter). The school have no clue what to do with the child, they put them in with kids a year above and they still get bored and are top of that class too. Perfectly well behaved, respectful, polite and actually love learning.
Do the parents sit and watch their kid be dragged down for the rest of their school life? they have been in to speak to the head teacher multiple times about the concerns but they aren't arsed, they couldn't even tell which kid it is because they go under the radar. They only know Jayden, Kayden, Mayden, Fayden, Gaydon, Yaydon who's dad is in prison,Mum will never work a day in their life and the kids have been doomed to fail from the moment they left their dad's ballsack.
Scenario 2.
Kids with actual SEN, I know somebody who sent their kid private because they had ADHD and slight autism and they just couldn't deal with mainstream school and the environment. Yeah they didn't "need" private school and weren't eligible for a special school (and probably wasn't right for them) but Private offered much better facilities for their needs, smaller class sizes let them thrive etc. Better setups for SEND kids and a lot more ability to give them a better support plan and work with them.
Neither kid was going to die if they didn't have it, however they would have just spend 16 years of their life just coasting by rather than being pushed.