In companies where I worked there were about two dozen developers for every product manager, sometimes more.

That’s why I said ”or whatever role”

1. There's far less product managers 2. What makes you so sure that product managers won't be automated away? The breathless pronouncements from the people running these companies aren't that there won't be software developers, it's that there won't be knowledge workers.

That’s why I said ”whatever” roles. Doubt you think no a single role will exist in 10 years?

As someone that as teenager observe traditional shoe factories being automated away, or the production being sent offshore, the robot factory can function with 10% of the original staff, or even less.

Now for the sake of argument multiply the 90% of the employees that were laid off, with the amount of companies that do the same, there aren't enough roles whatever those may be for everyone else now at the job center.