Shoes sizes have become the random walk of life.
On-line do what the ladies do with fashion. Order several items, the same styles in different sizes for shoes of course, and send back those that don't work out.
For people looking for comfort and wider fittings try Padders. Their sizing is pretty consistent too.
I'm not sure how well a computerised system could be made to work in a typical shoe shop without having over-complicated systems in place. To many try and not buy interactions. Probably impossible to get the minimum wage minions and Saturday helpers to go through a booking out and booking in procedure even if the system costs were viable. It might be something that could be made to work in a store the size of a warehouse.
Even then a "rock solid" system might constrain trade.
I was recently told a story about the aviation industry. An aircraft maintenance chap needed a part for a plane. Nothing too big or specialised but important to have it changed and working. His division's parts store did not have the part but the store for another division of the same company did according to their system. The plane was due to fly about 4 hours later so he checked with the other store, confirmed they had the part and could transfer it.
He said he would drive over an pick it up as the best option for making sure the plane would be ready on time. So off he went.
He got the part, checked it was correct and was then told he could not take it away - it had to be delivered to him via their multi stage parts management system which would involve several IT transactions with a wait time between each one and the use of the company's airport wide delivery service for security. All in all it was likely to take at least 12 hours and most likely the part would not arrive until the following day.
The chap left empty handed, the plane had to be kept out of service and, presumably, an alternative plane had to be found from somewhere or the flight cancelled. Such is the efficiency of what people think of as integrated systems.
Many years back I was visiting a client who complained that our Inventory and repairs tracking system had a serious fault and their stock counts corrections were going wrong again within a few days.
After printing a very long report relevant to the problem data and following a rather excellent evening wining and dining in Paris I spent a couple of hours poring through the printout and the problem became clear.
They were providing a service to a customer for rapid exchange of printers installed at the end of supermarket checkouts. The printers failed regularly. The target was a 12 hour swap service with the printers, individually tracked by parts movement and serial number, traced back through the transport system and warehouse drop off points to the centralised repair operation. And out again after repair. In other words the movements could be completely audited rather than just stock checked.
Receiving at a loication was, assuming the prior simply steps had been taken, a single click,. Got it ... but it also allowed people to create new serial numbers not previously know to the system - as you would expect for a repair company doing third party work.
It turned out that the chap in one of the receiving locations did not understand the system (nobody had "trained" him he claimed, and had decided that he needed to create a new record each time a printer arrived. Sometimes that was necessary of course. But where a printer had already become known to the system when he tried to create the record and enter the serial number the system would warn him. Not knowing any better he simply created a variation of the serial number and "created" a new printer. (Or sometimes misskeyed the serial number anyway with the same result - "standards" were not well understood at the time.)
So some printers disappeared for a time and new ones miraculously appeared.
After repair many items were correctly reported as "good" and came back into the system at the repair centre having previously been "lost" after their last known location in the transit route.
There were, of course, some simply procedural and training solutions to the problem. Or they could have looked at a more technical solution and equipped everyone in the chain with bar code writers and readers but I think the mobile aspect of that was not really available cost effectively at the time, unlike today. The scale of serialised item repair tracking they were dealing with could not have justified the cost and effort when compared with the need to "re-educate" one or two people at a specific location.
How many shoe boxes are extracted from their stock location, opened, unpacked, tried, rejected and then put back into the "system" on the shop floor waiting to be re-packed and returned to a store shelf somewhere later in the day? Each step of that transaction would, potentially, need to be recorded once the process analysts got to work.
Amazon might be able to work at that level. Not sure about anyone else.