That's true in practice with current radios, but it was a beautiful discovery in 2006 that it's not true in theory! In a world where radios are perfect and nodes cooperate to do decentralized beamforming, the capacity-per-node of a random mesh network scales as the number of nodes increases. See Ozgur, Leveque, and Tse, "Hierarchical Cooperation Achieves Optimal Capacity Scaling in Ad Hoc Networks," IEEE Trans. Info. Theory (2007) (https://arxiv.org/abs/cs/0611070).
Interesting. I wonder how well it would work in practice though. They assume uniform randomly distributed nodes, whereas people don't tend to distribute themselves randomly. They don't address practical concerns either, like how narrow the MIMO beamwidths need to be and how easy that is to achieve. Still a nice theoretical result.
This seems like it requires point-to-point communication; and with accurate MIMO configuration my intuition for the endpoints is that it's like they are communicating with laser-like narrow beams but in RF. But AFAIK multihop communication is still stuck at sqrt(n) scaling, i.e. not viable.
This is all pretty theoretical though, for a small number of nodes like up to 100 it should work pretty well like in the OP application.
(Also worth reading: Tim Shepard's Ph.D. dissertation from 1995 (http://groups.csail.mit.edu/ana/Publications/PubPDFs/Timothy...), which predates a lot of the "information theory" interest in this subject.)