To add my experience to the list:
I would say that it is worth getting a comprehensive set of tests, if they are available, but probably not worth redoing an MRI unless there is a really good reason such as it not being clear due to the fact that you were moving the first time.

If the MRI was done well the first time then surely repeating it will show up exactly the same things. It would be different if they were thinking about doing some sort of functional MRI, which might show up something more.

I think that all brain injuries are different, although there can be similarities.
In my own case, my MRI showen no abnormal structure in the brain. However, I specifically asked for a cervical MRI as well, because my neck had been injured, and that did show up a prolapsed disc. So, I would say that in my case it was worth doing. EEG and QEEG also showed up abnormalities, which were worth knowing about. Those test would be worth repeating periodically as they could show differences, hopefully improvements. Likewise, neuropsychological testing and balance testing can show up things. However, doctors are sometimes reluctant to test in case they find abnormalities, because they don't know how to treat them.

Personally I would like to know what was wrong even if that did not affect my treatment in any way, but that is a personal choice.

CS