OK, you have a point there... But let me ask you this. Why is no one accepting BTC payments through the Lightning network? We have several companies (mostly IT shops) that accept payment in BTC, but none of them accepts payment through the LN. Why is that? Is it that hard to implement that?
I don't have the data to back this up, but in my opinion it's mostly simply because not that much people are using Lightning yet(even though Bitfinex already implemented bitcoin deposits and withdrawals through Lightning, but maybe they just want to be the first exchange to support LN).
As for the difficulty of implementing lightning on a website, regardless how difficult it might be(I really don't know, because I haven't tried implementing LN on a website), if people want it, they would find a way to implement it no matter how complicated. It's mostly might just be the case that not a lot of people are willing to pay through it.
I think that (at least where I live) the biggest problem is not will the shop implement payments through LN. Shop must have fiat for all sells so they have to automatically exchange BTC for fiat when they receive it. That's where BTC payment gateways come in place and I guess when they implement LN, shops will accept it too.