Great, in theory - would not work, in practice.
There are a whole host of reasons why people miss appointments. They could be mental health related or a case of genuinely forgetting. I know a case of someone who did not turn up for their appointment because they could not afford the car parking charges!
You also mention about people being charged who use the NHS for non-urgent matters. While it is annoying that such people would do that, you cannot escape from the fact that people have different levels of what they would consider urgent. And this works both ways: someone who has a pain in their chest, thinking it is indigestion but it later turns out to be heart related, as an example.
I manage a few different teams. One of the teams I manage are responsible for finding out why people did not turn up for their appointment. I can't ever recall someone saying because they couldn't be bothered.
While it is VERY frustrating that people DNA, especially when appointments for the particular department I work in have a very long waiting list, fining those who don't turn up, or fining those who attend A&E on a whim, will further set back a certain demograph of people (in my opinion) and it would seem to be those who are already struggling.
I know when my children were babies, and poorly, I did use the emergency dept, only to be sent away with Calpol.
I have worked in the NHS for over 20 years and I would hate it to be a 'only the strongest survive' scenario, i.e., those who can afford to make their appointment, those without mental health issues, those who can afford the car parking charges.
Prolific DNA-ers should be discharged after missing a certain amount of appointments and, in some departments, are. And those who use the service for something they could have waited until they saw their GP, should not make a habit of it. But, as I said earlier, there are a number of easons behind this, rather than simply not being bothered, IMHO.