Most tradesmen are required to provide their own tools. I can see the arguments about security holding this back, but it's not an unprecedented idea.
More likely, employees would be forced to buy the one computer that IT specifies. And, knowing how much VB.NET code is running out there now, it'll end up being a top-of-the-line enterprise Dell laptop, crippled with XP and all of their network policies.
Somebody who's forced to buy a laptop and then give all control away won't be a happy body.
But having people bring in their home computers that might be virus-infected or part of a botnet to work? Err, no. I've had more than one home computer brought to me to fix and I have never once let them on the network. I don't need to find out that the next Sasser/Blaster/whatever is now rampaging through our internal network.
That's not to say that there aren't people and companies (likely small ones) that couldn't handle this. But unless each person was a pretty decent computer admin who was not likely to install crapware, kept themselves patched, etc., I wouldn't trust them at all.
But, like I said, I've seen the home machines of the people at work and I've removed viruses from them. There's no way I'd put them on our network even though I don't think there's anything they could infect. It's just not smart.
Ten years ago joining a major corporation gave you access to resources you didn't have on your own. Exchange was better than Yahoo mail. The T20 cost so much almost no one would buy it for personal use.
Today when student graduate they are often used to and already own Mac laptops or high-end PCs and are using Google services. They can lose productivity going from these (cloud) consumer to enterprise technology systems.
I recommend the Gartner report "Gartner_Report_BYOC_checklist.pdf" on BYOC.