What you’re describing for healthcare would be direct primary care with a capitation pay model.
Traditional wisdom is that about 1% of a doctor’s patients need care per day, so a doctor with 2000 patients should see about 20 patients per day. This is about standard for your office-based, 20 minute appointment doctors. For direct primary care the number per day is lower: for example, if the doctor does 1 hour appointments, you’d be aiming to see about 8 patients per day, with a panel of about 800.
The doctor is likely going to expect to be paid about $400,000, possibly more if they have employees working for them.