I was thinking of something more along the lines of how Tor works.

You are picked up at source, and dropped somewhere else.

Another Uber picks you up and drops you to your house.

Now, there is no person who knows both where you work and where you live.

One thing this does not solve, though, is that there is one person who knows where you work, and another person who knows where you live.

One thing this method of travel depends on, though, is that these two people don’t know each other, and even if they do, don’t know what the other person knows.