"Make transportation as reliable as running water, everywhere, for everyone."

I look forward to Uber Airlines in that case.

What would it take for a airplane to be able to pickup someone without stopping?

The army figured this out in ww2 to extract soldiers and others. Using a harness and pole attached to the rider, and catch cable attached to a plane, the rider is plucked at speed into the air. Much like the old air-mail systems. There are youtube videos of it.