Why does it have to fit on a laptop? Only miners influence which tx get into a block, not people on laptops.
>The problem that won't exist of billions of transactions?
Visa does 1 trillion tx/yr. Bitcoin tx is ~500 bytes That's just 500 TB/year. Miners with today's hardware can store that easily. A pruned observer node could run with just a few hundred dollars of hard drives even at Visa scale!
The bottom line is that Satoshi and others thought about this and no one saw it as a problem until Blockstream and other VC funded startups began pushing sidechains that they could profit from.