Why doesn’t each play start directly in the center of the field midway between the hashes, as opposed to some plays beginning on the right hash marks or the left hash?
Because it makes the strategy more interesting, especially when trying to get a last second FG.
Here’s a previous thread on the subject of hashmarks:
Prior to the introduction of hashmarks (1932), the ball was put into play from the exact spot of the end of the previous play; thus, if, on the previous play, the ballcarrier went out of bounds, the next play would be started just inbounds (and would require the offense to line up differently than “normal,” all to one side of the center (the lineman who snaps the ball). With hashmarks, if a play concludes outside of the hashmarks, then the next play starts at the nearer hashmark line; if a play concludes in between the hashmarks, then the next play starts at the spot of the end of the prior play.
There still seems to be some strategic value in preventing an offensive team from always having the entire field equally distributed on both sides of the center; having a side of the field that is “shorter” (i.e., less width available) makes it somewhat harder for a team to always just use that side of the field for its plays.