MRI's and CT scans after a concussion are done to look for and rule out an more serious injuries. Bleeds will show up on the 3rd day but usually not sooner. If they spontaneously stopped, they will be resorbed starting the 3rd day.

MRI's will not show the minute injuries from a concussion unless the MRI coil is a 6 Tesla or greater. The normal 1 to 2 Tesla coil MRI equipment does not have fine enough of a resolution. They will show a BB side item and sometimes down to the size of a grain of salt but nothing smaller. The diffuse axonal injuries common to concussion are much smaller. More like the size of a hair strand.

Doctors often use them to cover their own malpractice liability issues. The option is wise as it allows the patient to consider the financial cost. Insurance can also baulk at paying for an MRI that they deem is not medically necessary.

Getting stuck in that tube can be made much easier if you are prepared. I am claustrophobic but have successfully had many MRI's. The trick is to close your eyes before they roll you into the tube. Also, hold your elbows in tight so that you do not feel the sides of the tube. Now, think of something pleasant and spacious. They will give you ear plugs to help with the pounding noise. Use them.

But, as chitown said, a concussion without complications will result in a negative finding.