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Assuming that
a) The income coming from touring, streaming and selling records/merch is independent from the number of members in a band;
b) It's hard for artists to make a living through music;
It seems to me that there is an economic incentive to have the lowest possible number of members in a band, so that each member earns more money.
Is this is a thing? It seems logical to me, but never heard anyone talking about it. If not a thing, why?
Logically that's true. But musicians are all too often not much concerned with money. Getting popular tends to trump everything else. Also, the concert stages are often so small, especially when you're starting out, that "just fitting everyone on stage" becomes a concern, too.
However, if you look at successful power trios, for instance (Cream, ZZ Top, Grand Funk Railroad), I think the original three decided that sticking with "power trio" as the sound they wanted was the reason, rather than "Let's not add another guy to split the money with!"
If you add another instrument, then that changes all your arrangements, unless they're just doubling someone else. More to the point, the group dynamics would be drastically different: you all have to agree on things.
You'd have to decide that the additional sound is worth all the hassle. I'm thinking now of Sufjan Stevens, who has a whole bunch of unusual instruments in his band, and he definitely decided the additional sounds he could get were worth it (I don't know if they all get salaries or a cut, though).
You see the phenomenon in songwriting disputes. Robbie Robertson claimed all the songwriting credit for The Band, and thus he gets all the money. Modern pop stars often make gratuitous changes to the songs the producers hand them, so they can share in the royalties ("change a word, get a third").
So I guess the answer is "Yeah, sometimes, but not that often a primary motivation."
This is transparently true. As you add members, you need to a) tour more often, b) book higher paying gigs or c) accept smaller pieces of the pie.
But for musicians, as for most artists, money is rarely the primary motivation. Many, perhaps most artists subsidize their own career as a way of creating the art they want to create. Some artists want to produce solo music. Others are happy in a small band, whereas others like to be part of a big musical family. That, in turn, drives the kind of venues they have to target and the touring schedule they need to maintain. A solo artist, for instance, can play bars and tiny clubs, and make enough to live on. A group like Funkadelic, which has a rotating pool of twenty or thirty members, needs to tour constantly, and play more profitable venues (usually the larger ones).
Big artists, like Beyonce, tend to book only arena shows not only because they're famous, and they can, but because they have hundreds of employees working on their shows, and they can't afford to put a show like that in a smaller venue (unless it's a billionaire's private party!). A pop idol is essentially the CEO of a corporate enterprise (or its most important employee) and often will feel responsibility/pressure for keeping all the many people under them gainfully employed.
