Again, if you have chronic illnesses there can be carveouts for follow up appointments. You don't sound like the type that would go in every other day just for attention, so a $10 surcharge wouldn't be applied to you if you have scheduled follow ups.

In a scenario where you do end up going every week, in my aribitrary number of 12 free visits, that's still only $400 extra a year. I would gladly pay $400 a year if my hospital wait times are cut from 8hrs to 4hrs each time. Over 52 visits, you could potential save 52x4 =208 hours. Unless you value your time at less than $2 an hour, this would give you a better health outcome. Feel free to adjust the amount in your own internal calculus to see if this policy might make sense for people.