OK, there is something wrong with your install.
WooCommerce creates 4 pages on install:
Cart
Checkout
My Account
Shop
When you visit Shop, on the front end, you will NOT be able to click "Edit Page".
But on your install, you are able to do this.
Therefore WordPress is not treating this as an archive but as a page, and Views Archives cannot apply there.
When I create a Views Archive on a fresh install for Products, this page (Shop, which is the Products archive, slug "shop"), is styled by that View Archive.
The same goes for Product Taxonomies.
Natively the WordPress views archive will apply to all terms, no matter whether it's a parent or child or end point term.
I then added the WOOF Plugin, and it seems to have only a mode to display it as widget, is that correct?
So I did, I added a Price Filter, and that works fine.
Then I added a Taxonomy (Product Category) Filter and that works the exact same way.
So the problem on your install is not WOOF.
It's that WooCommerce is somehow corrupt and does not use an Archive but a page for the products and taxonomies.
I cannot solve that - the WOOF plugin works fine with Toolset, as far I tested it.
I recommend trying to fix the issue with the WooCommerce applying a "Normal" page instead of making it an archive, then this issues should all be solved, as the view will apply.