Yes, count me in.
I once thought of this when I rented a switcher for a three camera shoot. I knew On-Location would do a video capture, so why not more than one camera?
But here's the problem...
Up to the past couple of years when everything was still tape, most pro cameras ouput digital video over Firewire. It's pretty easy to get a 4-port Firewire card for your PC. And back then, it was mostly SD. In fact, I used two small Netbook computers with Firewire inputs and an external USB drive as a poor man's DTE with my Canon XL-2's.
But today, most pro cameras are tapeless and output the video over HDMI or SDI. There aren't many HDMI capture cards out there, and I think they are north of $500 for a single video feed. You'd need four of them (and a mother board with four free slots). And probably four dedicated SATA ports, each with a dedicated hard drive.
Depending on the video format coming over the HDMI feed, if uncompressed you'll need big fast drives to keep up, or a strong CPU to compress it.
Could be wrong, though....
The Decklink Intensity Pro Shuttle is only $199.99 and captures HDMI. One hard drive would be enough if it captures in MJPEG at 5:1 compression or even MPEG2. No need to capture uncompressed. If the CPU can be used with the GPU I don't doubt it can be done.