Hi @Kevin_Rey1,
Welcome to the forum! You seem very timely because we've had a lot of discussions about taxonomy, phylogeny, and their relationship recently.
You have hit on one of the fundamental frustrations of modern ecology: phylogeny and taxonomy don't line up. We (hope) that they're close, but most names are based off morphology-based phylogeny/taxonomy and modern molecular-based phylogeny shows that sometimes we got it wrong. There's divergent evolution, things we're not always sure about, and it's difficult. What's worse, we have this problem on a macroscale as well! I had a great (frustrated) discussion with a plant ecologist about this same problem last week. I'm goingt o recommend this post which talks about (some) of this.
(The part that starts from "We can infer taxonomy..." and ends with snark about chickens and dinosaurs is probably most relevant to you.)
Okay, so, if you have monophyletic clade, then the relationship between taxonomy and phylogeny should be closer. (Although not always) and sometimes, we shift names to try and get things up to date with the tree. Have you seen the recent paper about taxonomic updates based on phylogeny? However, most the way we do taxonomy in QIIME is to use a naive baysian classifier which is separate from the phylogeny calculation.
I think (maybe) the place where you're confused is that you're making the assumption that we should build our UniFrac distance based on the taxonomy rather than phylogeny? For UniFrac, we rely on that evolutionary relationship entirely agnostic to taxonomy. So, it's a calculation based on a nameless tree. I could, theoretically, do UniFrac on halloweencandy bars if I have a phylogeny relating them. (BTW, that blog looks like they have generally awesome posts and Im book making them for my "to read" list).
I'll also make the (brief) mention that "weighted" in UniFrac refers to weighting by abundance, rather than weighting by evolutionary distance.
Hopefully this helps untangle some of this? I also recommend looking at some of the previous issues that deal with why multiple ASVs/OTUs have the same name, because that might also shed some light for you?
Best,
Justine