I have terrible news about systems built on private health insurance (USA): it will still take 666 days to see a specialist, and you will need a referral from your PCP who may also decide they want to see you in person first. This may be its own scheduling nightmare. Then you may find out that your preferred specialist is out of network for your private insurance. The waits are a generally a supply and demand issue more than a beurocracies issue, but I can assure you that multiplying the number of beurocracies involved in getting healthcare doesn't speed anything up.