I probably should've left Chapman out of the original post. It wasn't my intent to make him a large part of the topic. My mistake. Live'n'learn.
Good post. I do have a habit of speaking partly in hyperbole, so I do recognize that one ball was, for the most part, used for an entire game pre-1920. At the same time, though, since the pitcher holds the ball more than any other player and delivers it to the batter, it's no secret that many (if not most) were notorious for doctoring the ball as much as possible in an effort to deceive the batter. Tobacco juice is another good example I overlooked in the OP.
And, of course, it's duly noted that the game has evolved since Lewis and Clark helped spread "Town Ball" across the continent. My initial point was that the overall consensus considers the beginning of the "modern era" as the time when the American League became the legitimate counterpart to the National League, and began facing each other at the end of each season. This is where I disagree with the consensus.
Primarily for the reasons I mentioned in the OP, I believe professional baseball most entered the "modern era" when gambling was eliminated and when the baseball was required to be white (i.e., no mud nor tobacco juice). The former is especially poignant, for no one knows how accurate and/or legit the scorekeeping, gameplay, outcomes, and stats were before 1920, since it's anyone's guess how many plays were made at the point of a dollar or a gun. For instance, I cannot be convinced that the Spiders were as bad as their 1899 record indicates. And that's merely one bold example. Sure, we all know about the 1919 World Series, but there's no way of knowing how many plays/games were made or broken in the name of a gambler for 50 years prior to that. It makes every single pre-1920 game suspect in my eyes. This is not to say every play or every game was fixed before Landis made an example of the White Sox. It simply means
we can't be certain which were and which weren't on the level before 1920, for gambling was, pardon the pun, a fixture in professional baseball for decades.
The virtually simultaneous change in the rules dictating the baseball remain white and unadulterated (certainly influenced by Chapman's 1920 incident) only serves to make the change in "era" more acute. If we add reasons Tyrus4189Cobb mentioned, some of which I hadn't even considered, and it's why I consider the "modern era" beginning post-1920 and not post-1900.

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