It seems to me that if a person requests WHF and then asks for accommodations to make their home more like their office, the company has a legitimate reason to deny paying for it. In my case, I was told to WFH because we've outgrown our facility and I don't have to be on-site to do my work.Do they supply you a computer, cell phones, modems and everything else for work? That will probably tell you what direction they will tend.
I've been considering asking about a standing desk. The other consideration is if I leave, or our office expansion plan is ever approved, do I want to have to give up having a standing desk at home? If it's company property then I can't keep it at home without working a significant number of hours from home.