It’s so much more complicated than that, it seems. Wool was a major business, even back then: https://www.cambridge.org/core/journals/urban-history/article/organizing-specialized-production-gender-in-the-medieval-flemish-wool-cloth-industry-c-12501384/A173396BD9F8E10E74634263506620BE

While I don’t think that article proves or disproves a woman being financially independent through spinning, it does hint that wool was extremely expensive and a huge business.