The latest high-end PCB tools actually provide useful autorouting features, because they have figured out that if you combine human ability to solve the difficult pattern-recognition and planning problems, you can have a computer solve the details.

For example, Xpedition's sketch routing feature: https://www.youtube.com/watch?v=fIi13gI9xEA

Routing 4094 signals sounds daunting, but it is a bit less daunting when you realize that a good fraction of them are power/ground (and route directly to planes), and the rest of them are mostly logically organized into buses/groups that can be routed together.