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The question seems reasonable to me, but I wonder whether two minor edits could improve it. One would be removing the characterization of Banach as lazy, and the other would be editing the title. To me, saying X wrote Y's thesis sounds like it means exactly the opposite of what it means here. (I.e., it sounds like it is saying X did the research, without making an assertion about who wrote the text of the dissertation.) So when I first saw the title, I thought it was an accusation that Banach's thesis was based on someone else's work. However, the question itself was clear.
Thank you, Margaret Friedland, for creating the meta thread; likely I should have done so instead of replying on main to Bok (but I was a bit short on time and got annoyed).
Regarding Henry Cohn's suggestion: I agree the title gives a wrong idea, one can/perhaps should also drop the laziness. (I would do so myself, but language wise do not find a good formulation. If somebody has a good idea I think they just should go ahead. When or if OP returns is unclear; new account last online 2 days).
Other than that IMO it is quite solid for a math history question, and as such well in the extended (though not strict) scope of MO. As such I answered (in CW, acknowledging the in par speculative nature) but will not start some "fight" if somebody wants to close it.
Perhaps "Who wrote down Banach's thesis?" would be a better title.