why does the game want me to install it to my hard drive?

I think it's the same as BF3, when you install to the hard drive it uses higher-resolution textures because it doesn't have to stream them from the disk. I can't say though because I install every game I play to my hard drive for wear-and-tear reasons so I installed before I even started.

EDIT: Though Battlefield 3 actually had a hard drive install, and then a seperate 1-2GB option to install the HD texture pack. I think Rage just includes the textures in the install.