in my marriage, I have always been the "too much stuff" person. I have watched lots of Hoarders tv show, and I can relate to many of the thoughts that the hoarders have. In the last few years I have been able to change much of my behavior (to be clear, I was never as bad as anyone on the show, no garbage or pests etc) but we've almost always had a room full of junk and stacks of things on bookshelves and tables.
In my experience, every nagging, frustrated, snarky thing that my husband said about my stuff just pissed me off and made me feel more overwhelmed and anxious. He has never once offered to help me sort or helped me go thru stuff. I had a garage sale last year and he refused to have anything to do with it. Im not saying you are being snarky or mean, but consider genuinely offering to help her assess the items.
If you watch Hoarders, watch how the interventionists and organizers actually help and talk to the hoarding people.
I agree that if there is a real use for the room, that might be motivational for her. Perhaps if you sit down and tell her how stressed and anxious it makes you feel and ask her to contribute some ideas to solve the problems, that might appeal to her.
In my case, I came into personal contact with a true hoarder, and it scared me. I also had some health issues and when they got resolved, I felt much more able to cope with organizing and downsizing. During the last two years I would say that I have let go of at least half of my belongings. Dozens of boxes in storage. I did a lot of it because I knew it was important to my husband and our relationship and living situation, so he was definitely an influence, but he could have been kinder to me during the process, imo. I still have hurt feelings about how he handles it.
So I guess my advice is, tread gently, with love and sincere desire for peaceful resolution. Try to really understand where your wife is coming from and her concerns. Try to come to a solution that you can both be happy with.