I am not sure if there's a superstition in the Japanese culture or just among the animators but according here,
In a lot of anime, a character (usually the protagonist) will show up
in the opening or ending credits, running along while remaining on a
fixed spot on-screen. The character could be running the whole time,
or start out walking slowly and gradually pick up speed. The
background is usually of the scrolling kind, but sometimes the
character actually seems to run through a changing scenery. In any
case, it's rare for characters to maintain a leisurely speed the whole
time; usually, this has something to do with either the pace of the
music, or the animators' need to keep opening and ending themes moving
fast at all times.
Side-on running and walking cycles are often created by animators as a
way to get a feel for the characters, and these cycles will no doubt
be used at some point in the show.