Semi-redundant post, but short of cauda equina syndrome a CT of the lumbar spine is gonna be faster, (significantly) cheaper, and in many cases make the diagnosis anyway.
At least in younger patients without horrible multilevel degenerative disc disease, if you give me a history of "concern for right L4 radiculopathy", I'll spot the disc herniation more often then not. For example: the 35 y/o guy coming in with acute back pain, I'm probably gonna see the disc herniation if i look hard enough. Granted, I fully admit that as a neurorad who reads 50-60% spine all day every day my eye is way more attuned to disc herniations on CT than a mammographer or other general rad would be.
At that point, if I've found the herniation and made the diagnosis, it's really back on you guys. I've done my job. The question becomes: would you do an injection based off CT rather than MRI?
From my perspective, if I can make the Dx on CT then the patient gets discharged faster. If you or whichever provider decides an MRI has to be done (for diagnostic certainty or whatever) it can be done at a low-cost MRI center on an outpatient basis. Considering the ER MRI wouldn't change management, I think it's best for everyone if the patient finds a low-cost MRI center and pays $300 instead of $2000+