I usually rent a Compact with Enterprise and receive an Intermediate or higher, except in FLL.
Last time I was in PHX, I got a Nissan Maxima because like you described I walked out there with an agent and simply asked to have that car.
At FLL, I lucked out once asking for a Ford 500 and actually getting it, the rest of the time I've gotten exactly what I requested except the cars were somewhat beat, like the Nissan Sentra or the Mitsubishi Lancer... both higher mileage cars with scuffs and dings all over.
Depending on the airport also, different locations consider different cars for different classes... like in ROC a Chrysler PT Cruiser was a Compact.
--Russ
PS. I too started using Enterprise because of their underage fee flexibility.