My mom was just sick and I took her to one of these. They did a strep test, a flu test, and diagnosed it as viral, which you can't do anything about.
Unless these quick clinics hand out antibiotics for viral illnesses or miss warning signs, they're much better than bothering another doctor with minor problems.
A viral infection can quickly become a bacterial infection which should be treated with antibiotics, particularly in the elderly. So for many people it is better to go to the same doc who has your medical record and knows if you are prone to certain complications from an illness (e.g., bacterial sinus infections accompanying a viral cold) or even complications to the treatment to an illness (e.g., allergies to certain meds). The Walmart-style clinic serves a purpose, but it doesn't replace having your own personal doctor who knows your history.
Even now that I do have medical insurance, making the appointment and taking the time off work can be a real bother. These are places to take care of hangnail type ailments, not to get a heart bypass.
Of course, I suppose I could learn Spanish, pretend to be an illegal (I'm dark enough) and just show up to the friendly freebie taxpayer supported ER.