"Please do explain why using Linux increases productivity for the average worker?"
I've got this one!
First up, it doesn't crash nearly as often. Boom, recovered hours of manpower right there.
Secondly, it has many many more features built in that don't require additional components or faffing around when you realise the attachment you were e-mailed needs an office service pack to be opened. Archiving is a great example. Windows will open practically nothing, and Mac about the same - Ark on the other hand will open pretty much anything you can throw at it, and it's integrated so the user doesn't even need to know what it is. PDF reading is another - Windows needs Adobe Reader, which I think we can all agree is magnificent bloatware. Every Linux distro I've used has an integrated reader, so again, no training or product knowledge required by the end user - just click the bloody thing.
Lastly (and these are just quickly off the top of my head) the file managers in anything that isn't Linux are atrocious. I thought Explorer was as basic as it could get, and then I used Finder. These things are terrible, and considering how core they are to the average office user's experience, it's pretty unforgivable. Something like, say, Dolphin, is brimming with useful and easily accessed functionality that helps me out on a daily basis.
Those are just the ones that sprung to mind. Others might be "having a network manager that isn't the most confusing labyrinth piece of shit ever designed by man", or "it's just way way way faster", but I'll leave those for other commenters.