Not sure how it is outside the US, but subscribing nurse-practitioners (requires just 2 additional years after a nursing degree) have been quickly replacing GP docs in the US for this reason. They'll send you to a specialist just like a GP would. It's all the same problems in terms of the underlying model, but the financial and time costs to the system are lower.

I'm not totally sold on what I'm selling though. My spouse has been a nurse practitioner for over 10 years; she had the option of becoming an MD but picked that route because she saw the grueling 80+ hr work weeks of older doctor friends and decided it wasn't for her. Unfortunately, she's still stuck with only 20 minutes for sometimes extremely complex patients that require a great deal of research and follow-through outside of work hours, and the extra slack in the system that is provided by her lower wages has just gone to hiring additional administrative middlemen that are seldom capable of actually filling in the gap, whether for reasons of liability, knowledge, skill, or motivation. These positions exist to try and ease the pressure on docs just like NPs exist to ease the pressure on docs, but it doesn't work because at the end of the day you need someone who can hold the liability (both legal and moral) and the knowledge (the correct diagnosis and the correct plan of action) within the same person.

Just like in software, where throwing more developers at a problem doesn't guarantee your problem gets solved more efficiently, for much the same reason. You need somebody who understands the domain, understands the tools, understands the business framework, and is ready to take responsibility for solving the problem. Each additional person introduces information overhead that makes each one of those tasks more complicated.