If if was disk space that DICE were shrewdly avoiding then the HD pack could have been installed to internal flash and the kind of USB drives that you can install whole disk images to. They also wouldn't have had about a Gigabyte of free space on the disk, and the HD install would have been at the very least a great deal smaller.
I'm not sure you really appreciate the brilliance of their HD pack.
The way things seem to work with this gen is you put a bunch of streaming systems into your engine, then you make a ton of content and spend the last month of the project cutting it down so it actually fits onto an Xbox DVD. (An interview about MW3 I saw described this process "we used to have 15 types of plants, now we have 12", etc.)
DICE completely avoided that month of work and corresponding minor downgrade in game variation with their HD install and second disc. When all your textures are guaranteed to be installed somewhere other than the DVD all of the sudden all your problems with fitting on DVD just go away.
There are two other things that make it smart as well.
First, say you fill up the DVD with as much content as you can and then take a few of your highest mips for textures of lower importance than others and drop them into your HD pack. People are really bad about noticing... for instance... the 1024 square texture they see without the HD pack compared to the 2048 squared one they see with it installed. So if they had done this, they'd have gamers going "why did I bother with this HD pack? There's nothing HD about it at all. It barely makes a difference. Stupid DICE." and on and on.
But they didn't do it that way. They make it so that the stuff you see without the HD pack installed is significantly lower res than you would see on a normal console game. When you install the HD pack, it's a night and day difference.
The second thing is me making guesses about how their streamer works. If you drop all of the streamed assets into the HD pack and have your low mips or always-loaded fallback assets on the disc, you have the option of
only streaming from the install media rather than the DVD. Kids don't complain about drive spin up during play, and you don't even have to test streaming performance off the DVD.
Seriously, they solved 3 or 4 common modern day game development problems in one blow, with the biggest cost (literally) being the extra disc. I expect to see a lot more of this HD install sort of thing as this generation wanes.
I obviously don't know the specifics but the restrictions on where you can install the HD pack are either a bug/oversight (in which case I'd expect it to be patched) or disallowed by Microsoft via TRC. I suspect the latter... it makes the most sense.
Edit: There may be something I'm missing here too... the choice to go with only low res assets in the non-installed version seems like it will screw over Xbox owners with no HDD, which I'm sure was a concern. In cases like those we have to assume that there was a technical benefit to doing it the way they did... I'm assuming it's related to their streamer as noted above, but also having a stark contrast between HD pack and no HD pack is a benefit whether it was intended or not. I suspect it was intended as DICE appear to be pretty good at manipulating gamer opinion.