There are several reasons, and mine are probably not the same as others.
#1: Image quality – This isn't just about resolution. You get a different "look" because of better corrected lenses with smaller
relative apertures at the same DOF as on a smaller format. The background blur is generally much smoother at the same time as sharpness is greater, which makes the images "pop" more. Local contrast is higher per image height and there are less artefacts (such as visible grain).
#2: Physical properties – SLR:s and TLR:s do have a much larger matte screen and thus in most cases superior viewfinders. This enhances the whole experience when taking photos. Also, handling the film (if we're not talking digital) and loading the camera is a very nice thing, especially if you develop it yourself too.
#3: Limitations – "Only" 8-16 images per frame is not a bad thing. It makes you concentrate more and you'll hopefully come home with more keepers at the end of the day. At least if you are not shooting some sort of action.
#4: Different aspect ratios – With smaller formats, you are limited to 3:2 (unless you step down as far as MFT or pocket cameras), which in my opinion sucks really bad. For many years I never found any focal length that I really liked, and now I understand that it was the aspect ratio that was wrong, not the angle of view. With 6x7 any lens will make me feel "at home". It just feels right. Square is nice too, but a bit challenging.
All of this has been a real eyeopener for me. I've never before enjoyed photography as much as I do now and I've never before gotten so many good images out of the times I raise the camera to my eye. This is what I've wanted since I started photographing, without knowing about it until recently.