According to a simple statistical analysis using computer simulations, a hitting streak as long as Joe DiMaggio's 1941 56-game streak is not the freakish occurrence that most people think it is.
More than half the time, or in 5,295 baseball universes, the record for the longest hitting streak exceeded 53 games. Two-thirds of the time, the best streak was between 50 and 64 games.
In other words, streaks of 56 games or longer are not at all an unusual occurrence. Forty-two percent of the simulated baseball histories have a streak of DiMaggio's length or longer. You shouldn't be too surprised that someone, at some time in the history of the game, accomplished what DiMaggio did.
I think there are probably some cumulative effects that are being ignored here though, like increasing media pressure/distraction, opponents trying particularly hard for an out as the streak continues, pitchers more likely to pitch around them, or even the streaking player getting super-confident. The first game in a streak and the 50th game in a streak are, as they say, completely different ball games.