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The overall performance of players over the course of a season will ultimately produce approximately that number. For example, if the league total for home runs is 5400, then the total home run output each season will be somewhere in the neighborhood of 5400.
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This is incorrect.
League totals are really not totals at all. They are values that determine the "rates" of the average pitcher/hitter matchup.
Prove it by taking a quickstart league and running a few years. Then restart a new league with the same quickstart league, but multiply all the league totals by 2, and run a few years. I expect fully that, despite the fact that your totals increased by 2, your actual performance in the two leagues will be very similar.