That's cool if you're down with OCD, but for the rest of us, why bother? One feature of HDMI is to run a digital signal for audio and video over a single cable. Connecting each audio and component feed into an analog-to-digital converter negates that one-cable, digital-only benefit.
Another "feature" of HDMI is its support for HDCP, and these adapters can't handle that copy-protected signal. What that means is someday, when a studio executive pushes a red button to turn on an Image Constraint Token for new movies, an HD-DVD enabled 360 will down-scale HD movies to DVD-quality; full quality in that future scenario will require a direct HDCP connection between a device and a TV. And some of our fancy HDTVs don't even support HDCP. Thank you, piracy panic.
Maybe Microsoft is preparing an HDMI cable to interface with the original 360's video-output port. Even then, the interface change won't impact games; it's only a convenience and movie issue.
Note that pictured adapter includes component to VGA cable.