When were these definitions formulated?
Multiple religions have rather strict requirements based on sunrise / sunset, for example, when one must start or can stop fasting, or when exactly to sacrifice a lamb (or a human in some religions). The definition has very deep roots.
Is this done purely because sunrise and sunset are the main examples of such events and it is easier for the naked eye to tell when sun is completely below horizon?
Wouldn't this offset the symmetry of rotations (since the "day" is always longer than the "night" by the duration it takes the background object to move fully below the foreground horizon)?
Daytime is not longer than nighttime in the middle of winter, in places that do have winter. The definition of sunrise and sunset does make daytime be a bit longer than nighttime on the equinoxes.
Suppose sunrise was instead defined as the time at which the entire Sun first appears above the horizon and sunset was instead defined as the time at which the first bit of the Sun drops below the horizon. Even with these extreme definitions, daytime would still last longer than nighttime on the equinoxes thanks to atmospheric refraction.