If you have access to the best healthcare you definitely don’t wait in the same queues. You have direct access to the specialists, often at the best teaching hospitals too.
Like Stanford pulmonologist in less than a week for an asthma eval.
Meanwhile, my Mom waited months on Medicare for a heart eval due to arrhythmias.
Whatever plan you have, it doesn’t sound top tier?
This didn’t require high net worth, just a better plan through an employer - or you’re in an area with low specialist populations? Or some sort of low priority on a triage schedule?
If you have mm net worth, the specialists come to you - quickly - unless you really need the .001% specialist. and chances are you they don’t and it’s not worth it.
But even Kaiser had no issues giving less than a week access for anything important.
The best you can do is concierge care, but that only expedites primary care everything in the US is about specialists.