Hello Ari, can you please recheck if you made any mistake or a typo error? Because it's well tested and works perfectly.
The edit product page is heavily customized by WooCommerce and it doesn't put any edit link on the product page. User Frontend also doesn't put any links on edit post and edit product page. But if you've already a edit post or edit product link on the theme, User Frontend only modifies the URL to forward you to the edit page.