I agree with some of what's being said here, but not the direction it's heading. Business-driven engineering is a dead end and it can't be patched by hiring consultants to tell people how to play planning poker. If you want to build great technology in-house, you can only do it as an engineer-driven firm.
The real lesson from all this is that you should never let people work on more than one thing at once. Make sure they know what it is.
Neat idea. Fails horribly in practice. Why? The problem with "one thing only" management is that the matter of who chooses each person's "one thing" gets horribly political, and fast. "One thing only" works only if the workers get to choose their one thing, which brings us to open allocation, which leaves me questioning whether we need all of this process that the engineers wouldn't impose on themselves...
Also, "one thing only" tends to create dead time and throughput issues, (a) due to communication issues and blockages, and (b) because people who'd rather have a different "one thing" will often do other stuff anyway. It also tends to lead to a high burnout rate when people can't voluntarily switch between at least two tasks.