It's actually a weird quirk of the health care system (depending on what country, I guess). The white cane is also sometimes called a long cane, or a mobility cane.

However, for occupational therapists and physiotherapists, a mobility cane means a support cane. And in some cases, clients request a longer cane for a variety of reasons (support canes are suppose to be measured to roughly the wrist). So calling it a long cane or a mobility cane in a medical setting can be confusing if they are thinking it is a support cane. And occupational therapists and physiotherapists don't always know there are more than one kind of white cane (ID canes, etc), so I have had to specify long white canes before in reports. It isn't common, but does come up sometimes.