Homeworking doesn't always work. But depending on the job/the individual/how much time is spent at home, there's no reason it can't work. Especially only one day a week!
If you can try and get some feel for why you think homeworking isn't working for others, it will help you come up with a strategy for making sure it will work for you.
Having lots of people working from home does give employers a bit of a challenge in terms of managing their health and safety, monitoring their equipment use, providing remote access to systems if appropriate, possible expense of phone lines/internet costs. Don't know if any of that would be a problem for your employer.
Lots of the arguments against homeworking apply when quite a lot of time is spent at home, lack of contact with colleagues, lack of 'face time' inability to manage a team remotely if applicable, that kind of thing.
My advice would be to meet with your boss, say you are appealing the decision as is your right. Say that part of the reason for your appeal is because they have not followed the required procedure in terms of specifying the reasons for the decision, part of the reason is because you disagree with the decision and don't think it's reasonable. In order to get a resolution to this, you would like to discuss with her exactly what her concerns would be, so that you have an opportunity to consider/address them fully.
I think that would be a very reasonable request from you, especially bearing in mind your employer hasn't given sufficient reason.
Consider offering a trial period for your proposal as well. That way if they feel it is 'failing' they can end the arrangement, so they have a safety net, but equally, you have an opportunity to prove how marvellously it will work and how much your productivity will increase...