A number of reasons.
Speed: No chain provides instant settlement, waiting for a block confirmation is untenable for simple API calls.
Granularity: No chain can support micropayments that are cost-effective.
Atomicity: You can accept fiat or shitcoins for payments, but then still have to sell those to buy Bitcoin which incurs its own trusted swaps and fees.
Businesses already run servers for websites, email, etc. A sovereign internet requires sovereign servers, the notion that you don't need a server is an NGO psyop. Lightning is simply the payments protocol for sovereign servers, no different than SMTP or HTTP.
Will most people use the Gmail or Godaddy of Lightning? Likely. It's the optionality not to that is what matters. Lightning.Pub and CLINK simply make that option easier to exercise than the status quo, that doesn't mean it has to be easier than not giving a fuck and letting the middleman do it for you.
