The demand isn't so much for Bitcoin payments as it is for low cost, fast and reliable payments. The fiat card payment networks and alternative fintech solutions that rely on them are all too expensive for small merchants. A café I was at recently (that doesn't accept sats) wouldn't accept a card payment for a drink either. The proprietor explained that he loses money on the soda since the card network 2%+25 cents is bigger than their margin. He'd said he'd happily accept sats if it was they didn't have these fees and it was technically simple.

Driven by this need, it seems to me that centralized LSPs (LN service provider), like Wallet of Satoshi, will end up being the PSPs (payment service provider) for LN payments. They can match the UX of most fiat payment systems if they wanted to and they can do this with much lower transaction fees than fiat networks.  Of course, this isn't the LN vision, but it will be the reality. However, it is also nice that LN is open and can be semi-decentralized as well, so while a few large LSPs will handle most payments, there is still room to hook in niche channels and nodes for other use cases.

Finally, the centralized LSP as a PSP is not such a bad thing as most of the value add from the card networks can be replicated as well, such as purchase protection.