The fact of the matter is that healthcare is already two tier. Dentists are a clear example, however, it extends also to MH care and to a lesser degree physio. I have back issues and can put my hand on my heart and say that a private physio has been head and shoulders above the NHS one I saw. Similarly £350 spent with a gynaecologist and their advice re HRT and dosage turned my menopause symptoms round and cut through the claptrap I was advised by my GP.
When dd was 15 she she was quite unwell. Harming by cutting and o/d, anorexia, depression, anxiety. CAMHS were woefully inadequate, offering six sessions of group therapy and closing the case when I said that was unacceptable. The GP told me to get her a counsellor off the Internet. Had we not been able to afford private care, I've no doubt she'd have escalated, dropped out of school, dashed her life chances and certainly wouldn't have gone to Cambridge and qualified as a teacher. At 27 she has recovered and manages her anxiety and the underlying ADHD that caused the issues. CAMHS only wanted to seek family problems and shift blame.
Fortunately, BUPA paid for a private adolescent psychiatrist, we paid for therapy in excess of £500 and the ADHD diagnosis and support. Had we been reliant on state support, I am pretty sure dd would have ended up as an in-patient due to escalation and her life chances would have plummeted.
I imagine experiences such as the above are replicated throughout the NHS system and am awareness people in their 50s who need knee/hip replacements and have lost their jobs due to waiting lists.