What eCommerce sites do you know that have a completely different structure than what you're used to?
It's just not as invasive as you want one to be.
That's the closest I can think of. There are ecomm sites that have been around since the 90s and haven't changed much but those either still have the product page/cart/checkout structure or are functionally just catalogues and require you to place an order by phone.
Additionally I would mention sites that only exist for RFQs (requests for quotes) and don't actually have pricing anywhere on the site. You load a bunch of items into what is effectively a quote request "cart" and then submit. From the backend of the system the business owners can then provide you with whatever arbitrary pricing they deem to fit. One of these sites on our platform is actually wildly successful but sells very niche product.
Also, I will mention the promotional products industry where there is an additional "decoration" step to the ordering process. Think of putting your companies logo on a mug. So not only are you buying the blank mug but you are also purchasing your decoration method of choice (screen print, digital print/full color, laser engraving, etc.) to get your logo/design on to the mug which has a complex pricing structure of it's own. There are many companies that have developed software to visualize what the item would look like with your logo before you even purchase it - some with pretty convincing results.
Granted it's a catalog site so they are going to have a huge inventory. Still I'm surprised how usable the UX is.
Radical anti commerce initiative dude.
Or maybe a bug..
Kool topic tho, keen to see the responses.