NHS triage is pretty effective: stuff that might actually kill you gets seen to immediately. Chronic conditions get managed long-term. The vast majority of the long waits are for things like hip operations, which will improve quality of life but aren't particularly urgent.
The US system is not without waits: https://www.nytimes.com/2014/07/06/sunday-review/long-waits-...
The latter.
In this case, the system which can get urgent attendance to all users wins over the one which does it only for a subset, even in terms of timeliness.
A system than turns non-urgent care (a cold or the flu) into urgent care (pneumonia) is going to 'stuff the ballot box' in its favor however.
- a) one where you would be randomly assigned to one of two groups: one which gets timely attendance for urgent and non-urgent needs; and the other one which gets no attendance at all, of any kind.
- b) one where all users get attended with an equal 3 weeks delay for non-urgent needs, and 0 delay for urgent needs.
It's not cognitive dissonance (unless on the part of public-health-is-better folks). Its a different metric. If cost is the only measure, then sure, 3 week wait for a free aspirin is 'good'. If its timeliness, then other systems win hands down.