I don't think it does either. At least for most schools-- although it is clinical, as you do have patient contact.
OP-
As an EMT Intermediate on a private ambulance, an ER Tech and an EKG Tech all in the Boston area, I hope I can shed a little more light on the situation:
If you live in Boston...your options are kind of limited for EMS. Boston EMS is a great organization, but opperates more like FDNY, or another fire service. It requires a physical agility test, a written exam, and other rigerous requirements. Also, I am nearly positive that most, if not all of their guys are medics or at least intermediates. Since there are no volunteer squads in the city itself (and I'd imagine none within 25-50 miles), your option as an EMT Basic would be to work for a private company (Lyons, Action, etc.). Unfortunately, this involves mostly non-emergent, BLS transfers from hospital to nursing home, hospital to hospital, etc. Don't get me wrong; these are okay, but after doing them for 2 years, I felt like I wasn't getting the level of experience that would benefit me for a healthcare career later down the road. All of this aside, I can't imagine a private company hiring someone who can't drive the rig. Unfortunately, you may often be in a position where you are NOT the highest level provider on the truck (as in, you're working with a medic) and the call is at the medic level. In that case, you would have to drive. Even with another EMT B partner, I imagine they would not be okay with driving all the time.
As far as ED Techs go; everyones right. I've found it does vary tremendously from hospital to hospital. I've applied for MANY of these positions, until I finally landed one. Here is my experience; some hospitals want a "tech". They will hire a basic, an LNA, whatever, and use them mainly to stock supplies and clean. At one interview for a tech job, my interviewer actually told me that "patient care comes second to organizing and stocking the department, if at all." This is a huge turnoff, and not a great way to get patient care experiencing. Some hospitals are much more flexible. Mine is one of the few in NH that allows their techs to work to their full "scope." As an intermediate, I am start lines, draw blood, do EKGs, etc. on my patients in the ER. I can also assist the docs and nurses with whatever they ask for, including chest tubes, intubations, etc. These ED Tech jobs ARE really hard to land though, becuase so many people want them. Still... it's a great way to get your foot in the door!
EKG tech is a decent job-- it's my third position I hold, aside from the EMT and the ED tech jobs. They usually pay well and are EXTREMELY low stress. However... as far as clinical experience goes, you don't get to do a whole lot (pretty much just EKGs!). So, the other poster is definitely right to say that there isn't a whole lot of patient contact! However... you'd see the code team work, which is good.
I would suggest you try an LNA course (or CNA, depending on where you're from). It's a bit pricey, but if you bide your time in a nursing home or on a med-surg floor, you may be able to sneak into an ER, or better yet, an ICU, or even a major hospital like Mass Gen. EVERYONE is always look for LNAs to hire. It's not always a pleasant job, but then again... nothing in healthcare ever really is!
If you have any more Boston-area specific questions, let me know!
Good luck!