My DH is a GP.
Honestly OP, you care too much. It's admirable but you have to change your thinking imo. I also work in the NHS in MH and a manager of mine gave me an incredible pearl of wisdom once. My job isn't to 'cure' everyone. That's not possible. My job is to do the thing I'm trained to do, to the best of my ability, with compassion, and let the chips fall where they may. Some will get better, some won't, but you absolutely cannot take it upon you to feel as though it's somehow in your control whether people will improve. They have to do the work themselves. It changed my whole approach, I adore my job to pieces and like to think I'm good at it, I always go above and beyond for clients and find time in my day to do the bits and bobs that will supplement their sessions and help them get the most out of it. But I can only do my 50%!
Is it possible to try step back a bit mentally? If you're not in control of who you do and don't see just take each appointment as it comes, do what needs to be done, and try not to worry/think about the people who haven't seen you yet? I don't worry about the wait list because that's not my problem. Just like when I worked at ASDA we were taught to only worry about the customer you're currently serving, don't worry about the queue, they're the store's problem. Work to rule, do your hours, do what you can in those hours, but don't break your back.
I've seen public health campaigns trying to educate people on when to see a GP and when to see a pharmacist and so forth, doesn't seem to make much difference though sadly. We need a whole change of mentality. A lot of the time the people who present again and again for extremely minor issues should be assessed for health anxiety and signposted for treatment for that. The person who's in every week with an imaginary bump or a tummy pain that's been checked out as being fine or who felt their heart beat a bit hard one night in bed has got an actual problem, it's just psychological. But there are also an awful lot of people unable or unwilling to do very straightforward things that would make a big difference such as lose weight, exercise a bit more, cut down on caffeine, stop smoking. The help is all there to achieve those things but people have the mentality that someone else external to them should be able to fix them. I'm not sure where that's come from but it's a huge problem. The people who are most successful in therapy are the ones who recognise early doors that they're the only ones who can 'fix' them, nobody else can do it for them. We can provide the tools and guidance and support but we literally cannot do it for them.
Bit of a ramble and I'm sure you've tried the above but I feel for you. GP is a pretty much impossible job. Then you get people complaining they're paid too much!