It sounds pretentious, but I think it comes from having multiple ways to compare things for similarity. Using the word similarity says what you are using the angle for. Angle similarity might work just as well until someone comes up with another angle based calculation. Cosine Similarity becomes a specific meaning indicating how it's caclulated and why it's calculated.

If you really wanted to be pretentious you could invent a Dimension Insensitive Euclidean Metric and call it DIEM to make it sound like you are putting some Latin into your papers.

I have a feeling it might be because the dot product of two unit length vectors is equal to the cosine of the angle between them.. but that's just a wild guess

I think the point is they're often doing it on things that aren't strictly vectors by definition, as in the physics sense, rather just some sack of stuff organised like they might be a vector and assuming its valid to compare angles because its just something numerically without much bias that does the job.

It is used as a distance function, so the important thing it is not that it is an angle, but that it is a similarity function.

And I think today it is preferred to call it "similarity" instead of "distance" because it is not a true distance function (15 years ago we called it "cosine distance").

As an engineer I find it funny when physicists (and general ML bros) don't know about linear algebra concepts