I think you might be onto something. If you look at Hungarian typewriters, you can see that the letters are already there, even if 0 and 1 are missing, which is typical of typewriters of that time:
I guess once one and zero had to be introduced with computers, it was thought to be too painful to remove those letters from where they were — and there was enough room on the left side at this point.
It seems that Ö and Ü are relatively popular, is that right? (Turkish had a similar problem, but they moved the letters elsewhere.)
It’s funny since zero on the left, before 1, kind of makes more sense logically, but most keyboards have them on the right.