Wait, what? No it's not. Not even remotely close. There is literally nothing about the bard that relates to European animism (or any regional animism). Animism, on a broad level, is the belief that spirits inhibit everything, from rocks to plants to animals to everything else. Even if you look at one of the more popular European animist beliefs, the fylgiur (Norse spirit animals), it's all about the animal spirits helping and guiding humans and the person having an intimate relationship with their animal spirit, where one affects the other.
In the Norse animistic traditions, it is less about having relationships with animals, and more about becoming animals. The many Bard class spells that accomplish shapeshifting can represent this well. The animistic traditions have strong relationships with the personas of natural features, such as mountains, rivers, ocean, thunderclouds, and so on, and here the spells that affect monsters (including Giant, Dragon, Undead, etcetera) are about right. Fey associations might help if more this-worldly. Meanwhile, much of the animism is human-on-human, where spells like
Project Image and mind magic work well. Healing is of interest. Psychic Divination is central, and the Bard class excels at this.
The Bard class can benefit to gain the
Commune with Nature spell on its list, as a way to represent directly interacting with the personas of mountains and winds, and so on. The
Mordenkainens Magnificent Mansion is actually a great way, to step into the inner world of a specific nature being.
Notably, Norse magic often uses speech to focus mental intentions. The warrior magic tends to chant meditatively and the shamanic magic to issue forceful commands. (Part of this tradition of speech is to avoid doing magic accidentally when the mind wanders with stray thoughts.) The Bard class is all about vocalizing magic.
The Norse vǫlva isnt really known for weather magic, per se, or other elemental magic. Albeit the Sámi noaidi is. The vǫlva might communicate with a nature being that is causing good weather or bad weather, and might even charm it or scare it.
Notably, UA allowing the Bard to choose its spell list, allows a player to build almost any animistic concept.
I'd posit the D&D bard is the opposite of animism, because the bard is all about people only. All of the abilities and powers are human centric. I can't think of a single bardic ability in D&D that centers around using mineral, plant, or animal spirits to help the party.
In the Norse view, humanity is one of the nature beings. And there are several kinds of nature beings. Corpses (of ancestors) count as a separate feature of nature.
The mechanics don't force anything. That would be your (general you) personal bias, not the game. If the class is basically, "most hp, all armor and weapons", like the b/x fighter is, that's not culturally specific. The problem you describe isn't one of "one size fits all", it's one of your own assumptions.
Heh, I cant help but notice. In your post, the assumption of what animism is − "animal spirits", "plants", etcetera − is itself an ethnocentrism that doesnt fully apply to some other cultures. The "mineral" somewhat applies in the sense of landscape features. Skyscapes and waterscapes are relevant too.