Restructuring URL

A retail site I am auditing has all of their products structured as www.domain.com/product-name and not www.domain.com/category/subcategory/product-name. Products are in multiple categories that are sensibly organised eg gifts, collections, by applications etc I can imagine that someone thought that its much easier to deal with this issue by just giving the products a direct URL with no need for rel=canonical! Budgets are not big for spending on development, there are other issues higher on the list, and the look and feel of the site are generally good so there is not major argument for redeveloping the site. If I were starting from scratch I`d suggest www.domain.com/category/subcategory/product-name and use rel=canonical to point duplicates to the page that would make most sense to rank BUT how much of an improvement are they likely to see by restructuring now? Its a magento site so I`m thinking it might not be too much work to get the products into a topical structure. Thoughts welcome.