Amrûnril
Hero
In the spell descriptions, to list the classes is waste of space. It is unnecessary − and is always untrue because subclasses and other features can gain the spells anyway.
I think it's largely a question of how one expects the spell list to be used. If one is browsing the class spell lists and then looking up spells based on those lists, then listing the classes in the spell description is redundant. If one is browsing the spell descriptions themselves for inspiration, however, then having the relevant classes listed with the spell is much easier than having to individually check whether specific classes have access.
I think the first use is likely more common, but I think facilitating the second use is well worth adding one line of text per spell.