It's true an LISW or similar wouldn't make the same rated as a PhD or an MD... but between the same "tier" of education in the provider, rates are surprisingly more comparable.
Insurers aren't more generous - they have negotiated rates. They're never paying 100% of what's charged. Some providers are better at negotiating, or have more leverage, than others.
You've shared a belief that a patient will continue to see a psychiatrist when not being given drugs. Since psychiatrists don't tend to do talk therapy, I will reiterate I don't believe this is correct.
I'm sure there are exceptions- a wealthy person might find a Doctor Frasier Crane type Doctor to do talk therapy- but they would be paying out of pocket. I know the local Ivy League school only takes a special Ivy League insurance offered only to the Ivy league school's students and staff. The wealthy- and their Doctors- don't need to worry about the "rules" set by insurance companies.
Insurers aren't more generous - they have negotiated rates. They're never paying 100% of what's charged. Some providers are better at negotiating, or have more leverage, than others.