The only priority of any sane health system should be to make people's health better.
If it cost nothing and the radiation carried no risk, nobody would have any problem with it. As it is, the cost is modest and the risk is low, so presumably healthcare waved their hands and said "close enough".
(That said I still decline pre-appointment x-rays when I do not believe they are appropriate)
In general, I find that patients have a sense that there is always a 'right' answer for what tests to order in order to diagnose their conditions. Some expect expensive tests to confirm a diagnosis that can be easily made at the bedside (like an MRI for sciatica for example). Others aren't interested in going through the difficulty of obtaining a somewhat difficult test like an MRI for a condition that is harder to diagnose at the bedside and would require further imaging to make a diagnosis.
The truth is that diagnoses are rarely 100% certain. How certain you need to be to make the diagnosis depends a lot on the risks of being wrong or missing a diagnosis and the risks of the potential treatment. For example, we want to be as close to 100% that someone has cancer before we give them chemotherapy. But, are willing to be less sure about diagnosing a cold. Sure, it could be the flu, but the risks and outcomes aren't that different.
The problem is that these probabilities aren't clear and doctors are humans and humans are bad at estimating with unclear probabilities. So there will be some doctors who estimate that the pain you were having that caused you to seek that doctor's opinion WAS enough to justify ruling out a fracture, because the risk of missing a fracture was worth the expense and very minor risk of radiation. Whereas the second doctor, may have seen things differently. AND this doctor has the added insight of the time that has past since your first appointment, ie you didn't get worse during that time (or maybe you did). That additional information of time, may have played into his estimation of the risks and benefit analysis for deciding on testing.
This is a good article to really understand the much wider than expected variability in professionals, including physicians. https://hbr.org/2016/10/noise
How can this be reasonable? It's impossible to know if imaging is required before seeing the patient, so it seems to me that a large number of these x-rays were unnecessary. In fact, the poster mentioned that on his last two visits he skipped the imaging and the doctor wouldn't have needed it anyway, bolstering my suspicion.
I could be totally misunderstanding, but it sounds like you are arguing that requiring imaging before each visit is reasonable. That just sounds way off base to me and like an easy way to ratchet up the cost for each and every patient.
Further, radiographs and MRI provide complementary information. Taken together, they provide much more definitive characterization than either alone.