The only way to scale beyond Visa & Co is to use second layers that aren't stressing the network and don't clutter the blockchain. Bitcoin's LN is already progressing and should be capable of processing millions of transactions per second. We still have to see how it works in reality and what its throughput is really capable of, but I'm very excited and confident. To add; Visa & Co use second and third layers as well, so we're definitely not unique in that aspect.
The only problem with the LN is that there is still the need to close the channel with a fee on the main blockchain unless we either raise the block limits bit or implement
channel factories.
If there are mobile clients available utilizing lightning, people won't ever want to deal with the main chain itself due to the significant difference.
This is one of the problems with LN.
We already have bitcoin which is hard to understand for like half of the world and now we add LN on top which I doubt most than 1% truly understand how it works.
So unless we have a client (app) that does it all for you with no stress then it won't be used globally (sadly).
This is the same with VISA, nobody cares what's behind the card, nobody cares that in reality payments have a settlement time, they use it because you can pay in 2 seconds with a contactless card and you're out of the store.