Still, it's not like historical geniuses all grew up as pampered aristocrats left to pursue whatever they liked. Many of them grew up as poor commoners destined for an entirely unremarkable life, but their exceptional brightness as kids caught the attention of the local teacher, priest, or some other educated and influential person who happened to be around, and who then used his influence to open an exceptional career path for them. Thus, if the distribution of kids' general intelligence is really going up all the way, we'd expect teachers and professors to report a dramatic increase in the number of such brilliant students, but that's apparently not the case.

Moreover, many historical geniuses had to overcome far greater hurdles than having to chase grants and learn a lot before reaching competence for original work. Here I mean not just the regular life hardships, like when Tesla had to dig ditches for a living or when Ramanujan couldn't afford paper and pencil, but also the intellectual hurdles like having to become professionally proficient in the predominant language of science (whether English today or German, French, or Latin in the past), which can take at least as much intellectual effort as studying a whole subfield of science thoroughly.

So, while your hypothesis makes sense, I don't think it can fully explain the puzzle.