A scientific basis for Open Source Software

That happens every day because there is little code sharing in academia. It is the other way around you know. When codes are shared, the general quality assurance level increases. Moreover, it allows codes to increase their complexity, reaching farther than earlier efforts did. This should be rather trivial to observe for anybody with knowledge on science today.

>And we're not speaking about codebases millions of lines long. It's quite rare for scientists to write large amounts of code,

First up, the fact that many scientists stick to more or less trivial implementations when they obviously could reach much longer with proper code bases available, only strengthen the point. Code needs to be shared, and it needs to be shared in such a way that one may build on each other. Scientists needing implementations as part of their research needs to give as much priority to the implementation as they do to writing the papers. Secondly, I am wondering what kind of experience you have in this. I can easily think of numerous academic code bases that comprise monumental implementations. Here is a nice selection at your convenience:
http://www.dune-project.org/
http://www.mcs.anl.gov/petsc/
http://www.openfoam.com/
http://www.reproducibility.org/wiki/Main_Page
http://fenicsproject.org/
http://www.gnu.org/software/octave/

Good luck with re-implementing any of them.