This strikes me as no easier than rvm, but less clean (installations go to /usr/local, no easy way to switch between various ruby interpreters or gemsets, harder to uninstall, etc.).
Why not just do this?
1) Update whatever requirements you need via APT tool of choice.
2) Install rvm
3) Install ruby-1.9 using rvm
4) gem install rails
5) Write great rails app.
It's not too often that you'll have a server that runs two applications. Sure, if that were the case then you would be using RVM in which case I would recommend following the guide already linked.
But if you've got one application running one version of Ruby, then this is definitely a perfect way to go.
Is rvm commonly used for production or just development environments? I can see where having a script to get your production (or testing) environment up and running with minimal user work would be useful, but if this is meant for just development I agree with your point.
I use RVM for both development and production, and I've written scripts that use it to set up both my development and production machines. It's nice to be able to reformat my workstation (for new Ubuntu releases, or new hardware) and get back to business quickly. As far as production, I'm not really sure RVM is that much of a win, assuming you're compiling the latest Ruby anyway and have only one app on the server. I use it since I've yet to learn proper packaging and therefore the only (easy) way to uninstall a Ruby is via RVM (I know about checkinstall, but IME it's buggy as hell).
I totally agree that you should become fully comfortable with setting up a box manually. But when you perform the same setup over and over and have the process memorized as I do then writing a little shell script to get the job done never hurts.
Why not just do this?