The problem with changing the 'free at the point of use' principle is that under any likely replacement it would continue to be free for expectant mothers, children, the disabled, and the elderly - precisely the people who consume the largest proportion of healthcare resources.
And that means that introducing per-appointment charges would likely have only a very minor effect on reducing waste & improving availability. Healthy people of working age would see it as imposing extra charges for no tangible improvement.
Either that, or you'd need to be looking at introducing a two-tier NHS, which I don't think many people would be happy with - "it might work in Europe, but what if it ends up being more like America?" would be the worry.
I think your point about the importance of triage to being able to running "lean" is a better place to look for improvements. The Single Patient Record ought to make automated triage a lot more reliable, for instance. And taking a broader view of ongoing health & economic impacts would help with your ADHD/autism assessment use case, as well as similar issues affecting people of working age (maternity care, being another obvious example).