I think a lot of what you suggest should "change" is already in place.
Health care is free in Canada and it would be hard to make it cheaper. I don't think you can say this all happened because the system failed.
Oh, the system fails all the time. I'll give one example.
Let's say a child needs a psychoeducational assessment. Where I am from, school principals have a budget and they determine how funds will be spent in their schools. So in a school of 650 students, only two students per year were selected. The kindergarten students would not be among the chosen ones, because kindergarten is not compulsory. Over the course of six years in elementary school, that child has 12 chances to be chosen. There are always new students coming in, and their needs might be considered more urgent.
If a parent has money, they can pay privately for an assessment, but this costs a few thousand dollars. Even if a parent has a good job with benefits, often the health plan will not cover these fees. There is a tax deduction for such claims. This isn't the full amount, and does little good if you don't have the money in the first place.
Let's say the child is the chosen one, and the school pays for the assessment. The child is now coded and has an IPP in place. Some codes are funded. Others are not. The child without the funded code may not get any extra help, like occupational therapy, etc. It's up to the principal. The parent may have to fight for every item in the IPP, like preferential seating, because some teachers won't cooperate, necessitating endless meetings with the teacher, principal and resource teacher.
If a child has a funded code, the school is allocated those funds. There is no guarantee the child will get any help. The funds go into the general budget, so the principal can decide to hire a specialist Phys Ed teacher or whatever. There is no accountability chain to ensure the funds are spent on the child for whom they are intended. The principal is not held to account, because the School Act makes them masters of their own domain.
Even a well-educated parent with a wonderful job, superior health benefits and plenty of free time would have a hard time negotiating this maze, if such a lucky parent exists. They'd better have high energy, too, because they'll need it.