NHS dentistry is a lot more .. honest about "we don't have any NHS appointments, but you can have the same service from the same person at a higher price, in which case we do have an appointment".
The number of doctors per capita in the US increased a lot for decades[0], but stalled over the past 10 years. I wonder if the blame lies at the AMA's feet.
For what it's worth, my personal experience with routine medical care hasn't been too bad in three (very different) states, though it's unclear to me what my expectations should be. It seems like the US is worse than average for primary care wait times and better than average for specialist wait times among developed countries[2].
[0]: https://www.cdc.gov/nchs/data/hus/2020-2021/DocSt.pdf
[1]: https://www.statista.com/statistics/186092/active-physicians...
[2]: https://www.oecd-ilibrary.org/sites/242e3c8c-en/1/3/2/index....