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From a programming/network point of view, what are the reasons why there are very few/no larger scale games than 16v16?
There are some 32v32 games but these are seeming exceptions to the rule.
Quite simply, scaling is hard and/or expensive, and O(n^3) is usually a pipe dream. For a game of 2v2, and a naive communication algorithm, you need each computer to communicate with ((2*2)-1) = 3 other computers (not counting some sort of connection mediation server), which comes to ((2*2)!/2) = 12 connections altogether ; likewise, for n versus n players, each computer needs to communicate with ((n*n)-1) computers, which comes to (n!/2) connections altogether.
That becomes ridiculous rather quickly, and other approaches are needed, such as “all players communicate with a central server, which provides them with updates”. That is slightly more scalable, but only up to a point. Calculating state for 64 players and communicating with them (and keeping the game state synchronized, even through short disconnections!) isn’t exactly simple, especially for games where latency matters (e.g. FPS).
Having massive server farms (with huge pipes to the net) which are dedicated and customized for this, can help, but it’s expensive (that’s a large part of your WoW subscription); if one of the players’ computers is doing this work, lags will become drastically more apparent – both for lack of processing power, bandwith, and latency.