> And that is the reason why universal healthcare will fail, and why the NHS has a private tier, and routinely pays for treatments outside of the UK, done in private hospitals.

This does not logically follow from what you said at all. The NHS has not "failed", nor does it have a private tier - it commissions some treatments from private clinics for purely political reasons. These treatments are still completely free to the patient.

An NHS hospital isn't receiving insurance payouts, so it has an incentive to treat people quickly and efficiently, with complete cures being preferred over long-term management when possible.