That reduces access but it doesn't affect the demand for healthcare.
I'm in New Zealand: not a heap better than you describe. Here GPs are overworked and getting an appointment is difficult. The health system has waitlists to control access to a limited number of procedures performed in each specialty. You need to be healthy enough to pass the access requirements and for acute surgery you need to live long enough to get to the front of the queue.
Depends how you define demand. People who need and seek care, or just those who need care?
Some people absolutely don't bother seeking care because they know they'll be denied care without a huge battle
At the hospital, they just classify your symptoms as “not critical”, refuse to admit you and kick you back to your GP, who then refuses to refer you for any investigations, I imagine because there is a gun to their head over targets etc
If your levels are high, you’re told oh it’s not severe. If it’s severe, you’re told oh it’s not critical etc
We have a system where everyone just gaslights you that you’re in fact not sick because you aren’t 3 seconds from death