It exists. It's called Amazon, it's called Shopify, it's called eBay, and it's called Alibaba.

They just aren't onboard with bitcoin and LN yet. Shopify is the closest, as they allow some bitcoin payment processors. The others, don't hold your breath.

The problem with self-hosted is ... where are your customers coming from? The online cart and payments are pretty much the tiniest problem for e-commerce. Getting listed in the search results on Amazon, eBay, Alibaba, etc. are why merchants use them.