Since emotions are best expressed through the eyes, they are usually made visible even if the character has bangs or wear glasses. There are exceptions, when the author wants to give the character a mysterious aura, or to hide the character's emotion momentarily. However, the eyes are usually shown regardless when it is necessary to clearly portray the determination of the character.
Being able to see the eyes of a character is important - but why put the hair there in the first place? This is to distinguish characters from each other. Disallowing hair in front of the face limits the amount of hairstyles that can be used. Also, the characters generally face the camera, meaning that they need to be distinguishable from the front too.
Generally, if the hair isn't completely obstructing the eye or eyebrows, it would be fine to leave out the detail on the eye, but it's become the norm in anime so animators probably don't think twice about doing it. It also saves having to worry about the eye looking odd when partially hidden.
In a forum post here, one user suggests an alternative way of drawing such cases, in which the hair gradually becomes translucent as it nears the eyes, so the characters expressions can be seen more naturally.
- No Transparency
- Gradual Translucency