Could we actually do this in a safe way? Having ill fitting shoes can cause a lot of long term damage. There could be a case that it's worth the X-ray risk...
But there's no real need to see the bones for fitting shoes. There's plenty of 3D scanning technologies today that do not involve ionizing radiation and would probably be more useful for fitting shoes anyway.
Having x-ray images or such would actually be somewhat helpful, as you could much more easily identify the metatarsophalangeal joints (the joint where the toe meets the foot), the locations of which do influence shoe fit to some extent.
However, the cost, safety, usability etc. of using x-ray machines in a retail setting makes it infeasible by a wide margin compared to optical measurement methods, and those generally take you far enough anyway. I'd rather go for dynamic analysis (i.e. scanning the foot while it is in motion taking a step) if more data on the skeletal structure is required.
As someone with hard to fit feet, I have often wished for custom footwear made with modern materials and design. I envision a system where you go to the store, they create a 3d model, you pick a design, and it is sent off to a factory that has been tooled to efficiently build the footwear from the model.
I think you could charge 150 or even 200% over off-the-shelf versions for modern custom fit running shoes/hiking boots/ski boots, etc. These markets already spend extra money for premium products. I know I would pay it, gladly.
Runners seem to go through shoes like clockwork. You could setup a subscription service.
This may be mostly irrelevant though because unless you have problems with your feet you can tell if shoes fit simply by the feel.
Perhaps most obviously, you just can't try a shoe on if you buy online. You can if you buy five pairs and return four, as some do, but it's a lot of hassle and a waste of resources for all the shipping back and forth.
Secondly, a significant portion of the population (tens of precent) have "problems" enough that most shoes in a store don't fit, meaning you have to try on a lot before you find one that does. And even if you don't have such issues, sizing between brands (and even styles) is so inconsistent that you usually have to try multiple different sizes to decide which one fits you. Having a 3D model paired with an AI system that tells you which shoes fit and what sizes to pick saves a lot of time for a lot of people, both shoppers and staff.
Finally, if you ever want to order custom made footwear, there is really no way around measuring your feet. And arguably the only reliably well-defined and repeatable way of doing that is to do a 3D scan to capture the shape.
Knitted socks are quite a lot more forgiving than leather shoes, fortunately, since the material accommodates by stretching when you put it on. I'm not surprised it worked well for you and your aunt!
I have the impression that this is half the battle with finding shoes myself. Probably the bones are the same size left and right, but I think they deform differently as I stand (or walk) in a way that depends on the contours of the shoe... and that sounds like a problem that would be hard to model with laser scanning or whatever.
I think it's more likely that it's the deformation of the shoe that is uneven than that the shoe affects the deformation of the foot much. An exception would be if it has a built-up sole with support for the arches, preventing the arches from collapsing.
Either way, it's a complex process that is hard to model, just like you say. The way we're getting around it is by collecting various data on what people end up liking and then infer the properties of the shoe, rather than trying to explicitly model it. So the solution is a combination of 3D scanning and machine learning.
Also worth mentioning, by the way: most people actually have slightly different size and shape on their left vs. right foot. For about 50% of the population the length differs by more than half a US size. Being perfectly symmetrical is the rare case.
Randall Munroe's radiation dose chart (https://xkcd.com/radiation/) says that a cross-country flight delivers a higher dose than a typical dental x-ray or even a chest x-ray. Maybe it would already be worth it with really modern imaging equipment.
The X-ray image can't possibly tell you things like that the shoe's upper is too tight over the metatarsals, or that a seam inside the shoe is rubbing on your pinky toe, which will cause blistering.
At the end of the day, a good shoe fit is a simple matter of feel.