I have paid to go privately before when I had very bad acne and didn't want to wait 5 months just to see a specialist. That was affordable but still cost near £1,000. Going private for small things might be fine, but for more complex operations or situations where you must be an inpatient will cost you thousands of pounds. For example, my dad needed a back operation that would have costed him well over 6 grand to go private (and avoid the 6-month NHS waiting list). Cancer treatment would cost a fortune, you'd need to cook meth in an RV if you didn't have private insurance. (To be fair the NHS is quite good when it comes to cancer treatment.)
I guess it's just something which is reassuring to have. Knowing that you can go private for any matters, small or large, is a nice feeling. Not to mention that the NHS is struggling.
It's a personal choice, I can understand it's not for everyone.