This wouldn't work if the software requires a kernel module that isn't packaged for your distribution. It also wouldn't be particularly useful for a file system navigator or something that needs to see the rest of the system. That should still leave in quite a bit of useful software.
Wouldn't that negate the benefits of things like shared libraries?
..comes to my mind. Shared libraries and their advantages are at least.. controversal.
-Sun presented a paper saying it wasn't worth it
-Plan9 doesn't use dynamic linking and some of its utilities have smaller binaries than similarly named utilities on FreeBSD
-People like dynamic linking for the same reason they believe in god
-Statically linked binaries aren't as portable as one would like.
It reads like more of a rant to be honest.