Hello!
To address “why” first, it has to do a bit with history, and a bit with logistics. Up until very recently, the image of a scooter was this:

More of a cart than a scooter, used by the elderly to get from their house to their grocery store. So, most of the rules were made with these in mind, not the modern ones available now.
However, since the modern scooters have not caught on here (likely due to restrictions on trains!) and there has been little effort/pressure to change the laws.
Many trains and stations have crowded platforms and being able to maneuver on the spot is often necessary. These older scooters cannot easily turn sharply and doing a 3-point turn on a train or platform takes space and time.
So, that is why they were blanketly rejected.
However, thanks to foreign visitors, things are improving. Even the shinkansen (notorious for refusing scooters) now has guidelines for scooters it accepts, and there are certification badges for scooters bought in Japan.
As to whether or not it will be allowed, that seems to be random. As with anywhere, rules are on paper until someone applies them. So, if a staff member is a stickler for the rules, you may be refused at less accommodating stations, where as other staff may not care about the official rules. But I have heard from others that they had no issues.
If you have the option to bring a wheelchair, it will be safest. If you want to bring your scooter, you will likely be OK, but must keep in mind that some rule-abiding staff may approach you…
I know it doesn’t really answer your question, but it does still seem fairly random.