Bitcoin onchain transaction processing rate is ~5 tx/second. Lightning comes to help for majority of transactions like daily purchases, but one still has to go onchain to open at least one channel to ensure their sovereignty. And this ends up with a limit of ~150M tx per year for 8G world population... that meas an average person would barely afford opening a single channel during the entire lifespan, leaving aside possible problems channel issues. That obviously does not appear sustainable.
What do I miss? Do we anticipate some kind of 2nd level solutions to circumvent that? Of course we're talking about rather far future, but is there a rough understanding of how it is going to work on such a timescale?