As an EEE with free days, I've never had a problem if I go and reserve the most expensive SUV/Crossover class I can find. I've taken an Enclave from Seattle to Spokane ($1700 list for 6 days, total cost $70), an Expedition from DC Union Station to Philly ($299/day, net cost $0 plus the extra driver fee), an Equinox from RDU to DCA, etc.

As an EE or EA, I could see them possibly not wanting to get rid of a vehicle which they have a good record of upselling people into.