Every prescription I've received in the last several years had two signature lines. If the doctor signs on one, it's "dispense as written", and if they sign the other it's "substitution permitted". So it's not like they have to do something special to get DAW.
But how many of the prescriptions you received had the signature on the DAW line? It's typically very uncommon.
In fact, in the hospital setting, a portion of a Physician's reimbursement is tied to the ratio of generics to brand name drugs that their patients were given.
I'm not sure if this is the case for outpatient stuff, but internists are absolutely incentivized to prescribe generics.