It's possible right now. The solutions just aren't ideal ... and probably won't ever be.
There's W-VHS ... which works just like you described (like a VCR). Capture the analog signal in a way that can be played back. It's relatively inexpensive (used units have been found in the $1k price range). You've got component inputs so you can record from anything out now ... don't have to worry about DRM ... etc. But, you've got many of the same drawbacks as VHS analog recording ...
http://pro.jvc.com/prof/Attributes/f...l_id=MDL100250
The more elegant solution is to caputure digitally (like a DVD-R). However, this is where things get very expensive. You either need the hardware that can handle an uncompressed digital stream (hard drives , CPU, etc.) OR you need to compress the stream up front. There are several products out there that can do this ... taking either (or in some cases both) approaches ... but they are VERY expensive.
Yes, the technology will improve / become cheaper over time but ...
The cheapest / most elegant way to record HD is going to be to capture the original, compressed stream. It's hard to see where a DVI or component recorder is ever going to reach the production levels needed to drive prices down ... when a Firewire recorder is always going to be cheaper and provide better picture quality.