The block chain is a single channel broadcasted over the entire
world, and I don't believe it will ever be possible nor desirable to broadcast all the
world's transactions over one channel.

The everyone-validates-everything approach doesn't scale. It is however
useful to settle larger transactions in an irreversible, zero-trust way.
That's what makes the bitcoin system, as it is now, valuable.

But it is absurd for the whole world to have to validate every purchase of
a cup of coffee or a bus ticket by six billion others.

Naively scaling up the block size will get some leeway in the short term,
but I believe a future scalable payment system based on bitcoin will be
mostly based on off-blockchain transactions (in some form) or that there
will be a hierarchical or subdivided system (e.g. temporary or per-locale
sidechains).