Except now I have to jump through hoops with HR (let's just assume they'd be OK with this, which they almost certainly won't), get the contract in place, work with IT to get your environment set up, and bring you up to speed (so really I may get one full day of actual work)... just to realize that I don't want to hire you. Oh, and did I find you through a recruiter? Now I have to pay them a cut. Do I now get to run this little bureaucratic maze for all N candidates I'm looking at? You have become a very expensive interview across at least three departments and you're probably not worth it.
Sorry, but no. I do ask for some whiteboard coding, but it can be done in any language (or pseudo code) and I'm really only trying to tease out your thought process. For a junior or mid level position, yes; I am also trying to figure out if you can write a line of code. I'm also not sure how you're going to be able to get away from your current job for an entire week (I have literally never interviewed a candidate who wasn't fresh out of college who was unemployed at the time).
I agree that it can be a pain, but there aren't always better ways to measure your ability to take a problem and turn the solution into an algorithm.