It's fairly standard for clear coats to go on the side of rosewood/ebony fretboards but not the top. Commercially, it's easier and quicker (i.e. less cost) to just mask the top of the fretboard when spraying clear coats than the top and sides, where far more precision is needed.

If you've got a paint finish on the body, then having clear coats on the side of the board can prevent the feeling of a paint ridge along the edge, and the finish can fill in the gaps around the fret ends, giving a smoother feel in the hand. With a stained finish, a paint ridge isn't an issue, so it's then personal preference.

I like to put finish in the sides as I feel it provides some extra protection for the edge of the board, plus I like the look.