On the more dynamical side:
- Doyle & Snell. "Random walks and electric networks" (1984).
- Lovász. "Random walks on graphs" (1993).

A few important but overlooked papers prior to Watts/Strogatz and Barabasi/Albert that come to mind:
- Cartwright & Harary. "Structural balance: a generalization of Heider's theory" (1956).
- Molloy and Reed, “A critical point for random graphs with a given degree sequence” (1995).

That said, my main reference when thinking about communities is precisely your work on descriptive vs inferential approaches that you mention, so I will probably agree with you on most aspects :)

But at the same time, I think it's nice to keep in mind that there are situations where looking at disconnected components as a extreme case of communities can make sense, especially if the objective of the study is not to analyze data.

I completely agree, mixing two conceptualizations of community can lead to problems, because minimizing cut-sets and maximizing likelihoods are based on very different assumptions.

To be clear, I agree that interpreting community detection as a maximum-likelihood problem is a more powerful approach to understand complex datasets. My point is that, from a mathematical (not statistical) point of view, the other vision can be insightful too.

In fact, I would say the pure-math approach to communities tends to understand them as "almost disconnected" regions (partitions with a small cut-set), and this perspective has led to nice results (for example the Cheeger inequalities, the spectral clustering algorithms, perturbative methods, etc).

I think the interpretation of communities as network partitions with a small cut-set is useful in certain areas. Ofc, claiming that this conceptualization of community is statistically meaningful is problematic, but as a descriptive concept I think it's ok.