"Multitasking" is not a skill. It's a PC word for "can't stay focused".
I grant that being able to handle multiple sensory inputs would have to be great for playing video games or driving an Indy Car. In the workplace, it's hardly an asset. Our best programmers do not multitask. They have focus like you wouldn't believe.
Our younger workers who pride themselves on being great multitaskers (by their own admission during interviews) do not seem to be able to do work with depth. For example, a quality training document will probably need 3 thorough revisions. The "multitaskers" bang out a first draft, skim it over once with some edits and pronounce themselves finished. Then when I send it back with a couple things to fix on every page, they are surprised at how many things I find. I tell them that 90% of what I found should have been fixed before it got to me and it's actually sloppy work. They had all the time they needed to do it right, but they can't stay focused.
I think it was a recent issue of Fast Company that had a cover story about the guy who unplugged from everything for a month - he even stopped tweeting pictures of what he was eating for dinner!

. And he was amazed at how much clearly he could analyze things, among other benefits. And Fast Company is typically a magazine that has an attitude that "good enough is good enough" and doing 10 things half-assed is better than doing 3 things right, because speed is the most important thing in business. Their heroes are people who start a company while in college, using college resources, have three blogs, tweet 10 times a day, speak at entrepreneur events every month, and work out of their apartment so they can work 18 hour days and not have to commute anywhere. They never question whether they could have a more successful business if they only worked 10 hours a day and skipped all the other stuff that is just sucking up their time.
When people begin to understand that multitasking is not a skill or a necessarily desirable way to exist, maybe we can all benefit.