I have never tried using portage with binary packages, but I am using Paludis with binary packages since a while and I have to say it is very different from using Apt or Pacman.
Package managers which are build for source packages (e.g. ebuilds/exheres) have a much more complicated logic running in the background, come up with much harder to solve problems and are a lot slower (orders of magnitude).
The only aspect where this setup is superior than e.g. arch + pacman is when it comes to using source packages on the same system. So I guess that is nothing you would like to use on a Chromebook anyway. Therefore, using a Debian container is a reasonable choice, in my opinion.
ChromeOS/ChromiumOS uses portage for its build system, to produce a signed, read-only image that the OS can boot from. CoreOS uses the same tooling FWIW: http://www.chromium.org/chromium-os/build
This is why you can’t just install random packages onto the parent OS. Any additional software needs to run in some overlay filesystem or sandbox.