I think there is a big difference here between non-compete and no-poaching agreements. At least yours is tailored to a radius, but I don't know that your narrow definition of non-compete is really the same.
In principle, I agree with you. However, in practice, a lot of what drives non-competes is concerns about poaching. I don't know if non-competes are particularly prevalent in service industries but I'm probably most aware of examples from consulting. I'm not going to defend non-competes but I suspect one of the reasons that they exist is that poaching clients and use of inside knowledge from a former employer are difficult to prove if they're not blatant whereas working for a competitor is pretty straightforward.
I think there is a big difference here between non-compete and no-poaching agreements. At least yours is tailored to a radius, but I don't know that your narrow definition of non-compete is really the same.