The bottleneck in the MRI machine is the human.
An MRI is a big bubble of a very flat magnetic field, whose strength determines the frequency the the atoms would oscillate at.
The highter the frequency, the stronger the field is needed, but the higher is the resolution.
To make an image, a gradient is introduced in the magnetic field, making it possible to distinguish from where in the slice the signal came, based on it's frequency.
The received signal is passed through a spectrum analyzer kind of thing, and the spectrum is the bright and dark spots in the line of the image of that particular slice.
To get the next line the gradient must be altered, shifted in space. Line by line, slice by slice.
As you all know, a changing magnetic field induces a current in the conductors located inside of it.
And a human is both quite conductive and is a sensitive electronic "device".
So how fast they can cycle through the lines is limited by how much induced current is safe for a human body.