Why does bond length decrease with increased basis set quality for SCF methods?
I think that your rationale is right. I would think it in terms of energy instead to make a little more precise. Thinking about a diatomic molecule, the nuclei-nuclei repulsion function of distance does not change with the basis set used. So the difference is strictly in terms of electronic part. At large distance the atoms behave more similar to an isolated atom, so few spherical harmonics are enough (for a relative description). As atoms get closer it is needed more flexibility to represent the very different probability density that there is in the space region located between atoms. With a smaller basis set this wave function is approximated poorer. If so, it is expected that the energy rises in such region if one consider the variational principle.

Here I calculated for the oxygen molecule in the region close to equilibrium distance (about 1.2 A) the difference in electronic energy between HF/STO-3G and HF/6-31* basis set:



The behavior close to 1.4A should be just an artifact in convergence (I did not take care about that). 

Sadly I never found a discussion about that in the literature. Up to my understanding there is not to much that can be said about that.