Rollonsept it would make no sense to have people unnecessarily seeing more expensive workers or workers whose time is more scarce, if the care could be SAFELY delivered in a way that more efficiently allocates resources. I emphasised the safety aspect in my first paragraph because that's extremely important and that's a truly massive if. But WRT the general principle, it's difficult to run an organisation without wasting large amounts of money, if you routinely allocate tasks to more expensive workers that could be done by less expensive workers. (Though sometimes more complicated task allocation can be expensive too, or the expensive worker might have spare time and it's not worth employing an extra person for a few simpler tasks, or there are reasons you might want one person to do all parts of a larger task including the simpler bits, or you might want to avoid packing your most qualified workers' days with only the most extremely difficult, complex tasks. It's complicated. But generally, you don't use a highly-qualified, highly-experienced, highly-paid staff member for a lot of work that can be done by someone less expensive.)
My second paragraph was discussing why in practice, that's a more complicated issue than it seems in primary care, when the person who has to make the decision as to who to request care from is usually the patient, who generally has no training at all. People often don't know what they don't know, and that includes patients, nurses, PAs, paramedics, pharmacists, GPs, specialists, whoever. It might be easy to confidently say to yourself "This problem can be safely dealt with by a person with a lower level of education, experience and accountability than a GP" when in reality there's a big invisible flashing sign that says "needs a doctor" that only a doctor knows how to read.
But the basic principle of allocating tasks efficiently to workers, so that you don't have unnecessarily costly staff doing tasks that could be done by someone with less training and experience, is a sound one. There's a reason that GP blood samples are usually taken by people who are trained just to take blood samples (and paid commensurately with that lower level of training). The vast majority of the time taking blood samples doesn't require an RN or a GP, it's fairly easy to identify who can safely be sent to the phlebotomist for blood samples, and, importantly, the person who ultimately decides whether it's safe for that procedure to be carried out on a patient by someone who is only trained to take blood samples is the GP, who's qualified to assess that.
Ideally, I very much agree with you that the best thing for primary care in particular, where a patient presents with a previously unassessed problem, is for a GP to assess that presentation. Anything else is less safe. Something that looks minor and routine to a patient, a nurse, a paramedic and a PA may set off klaxons for a GP. I want everyone to be able to have a GP assess their health problem whatever it is, and for other healthcare workers to be used to deliver care only once the doctor has decided that's safe and appropriate (like my annual nurse asthma reviews, my phlebotomist blood draws, or the physio I was referred for when I had a sore leg).
I'm just trying to say that I can see why surgeries would want to try to make the most of the limited, scarce, expensive resource that is GP time. I understand that many surgeries don't seem to be able to handle the need (I hate "demand" in this context, it sounds like patients are trying to grab resources unnecessarily) at the moment, and that they might be trying to find ways to redirect patients who may not require someone with GP-level expertise to other healthcare workers, whose time is less scarce or who are less expensive to employ.
The way some surgeries seem to be trying to do that at the moment is by coercing people into nurse appointments even when the patient knows that it will end up having to go to the doctor anyhow, or deceiving patients into thinking they'll be seeing a doctor when they won't, and other similarly shitty tactics.
As you say, this often only ends up wasting time in the long run anyway, and as the OP's experience shows, is very unsafe.
As I said, my preference would be for a GP to assess first, always, because medical assessment and diagnosis of randoms walking in off the street is extremely difficult, pressured, and dangerous — riven with traps for those who don't know what they're looking for, and pitfalls for people following protocols and flowcharts without the extensive knowledge and experience, and ability to think in certain ways, of the average GP.
But if they absolutely have to funnel any first-contact patients to non-GP practitioners, I would much rather they were completely upfront with patients, telling them exactly what kind of things these other workers are able to confidently deal with, and what their limits are, and let patients themselves choose to see these workers. I think surgeries are treating us all as grabby stuck-up people who demand a doctor regardless, which is why they resort to lying and force. But I think that if they informed us properly about these other healthcare workers and what it might be reasonably safe to go and see them for, it would be no less safe than the force and lying approach, and would result in less waste and duplication.