Some sequences such as EPI [1] can get images very fast (200ms) with a trade off in spatial resolution. This is for things like cardiac imaging where low resolution images of the heard every 200ms are more useful than a single high resolution image. Also for moving parts of the body there is often blurring artefacts due to movement within the image window using longer sequence types.
Unfortunately I think the biggest inhibitor of MRI being more common is still the price of a scan. Here in Australia it can be a few hundred dollars for a scan (and I understand it can be far more elsewhere). Again though if we had access to a cheaper option the idea of regular scans may not be too far off.
I like to imagine a point in the future where the sci-fi full body diagnostic scanning is a reality. Still a lot of work to get there but it is certainly getting closer.