What is the purpose of a doctor referral?

They have data that says that if your primary physician is maintained as a gatekeeper, it cuts down on utilization.
Less utilization, more money for the third party payer.

If your insurance requires a referral, it’s basically the primary doctor telling the insurance you need to see the more expensive doctor.

If the specialist requires a referral even though your insurance doesn’t, it’s the specialist wanting to make sure you are worth his time, and you really need his special services.

It’s to make sure that whatever’s going on isn’t a minor issue that your GP could handle.

It’s to create a hoop to jump through. If you forget the referral (and they know x% does this) then the insurance doesn’t have to pay, then the insurance companies get to give themselves a nice bonus with the money they would otherwise be spending on the healthcare of their policyholders. Isn’t capitalism great?

And, what @gorillapaws said. Yeah, that too.