I think a counterargument to this is that, in a way, a mythological creature is the "property" of the culture that created it, and that should be respected as much as possible. Obviously unicorns don't exist, and so a discussion about what the most accurate depiction of a unicorn is is fundamentally fallacious to begin with (I think this is partially your point, correct me if I'm wrong). However, I think in the context of fantasy media, such a discussion might actually be warranted in the same way that if I were to, say, make a fanfiction about Pokemon, I should try to be as accurate to the source material as possible purely out of respect. The debate here is exactly what the source material is, and in many cases that's tough to determine because a lot of mythological creatures such as unicorns don't have a clear-cut origin.
Say I wanted to determine the origin of a Pokemon, well, that's easy. TPC owns the rights to Pokemon and are, for most intents and purposes, the original creator of said Pokemon, so any media or literature produced by TPC can be said to be the most accurate depiction of what a specific Pokemon is. If I were to make a Pokemon fan-fiction, and decided that Arcanine is a Fairy-type for the purposes of my fan-fiction, I think most people would agree the original Fire-type Arcanine is "more accurate" (for lack of a better term) than my Fairy-type one, despite the fact that Arcanine doesn't exist and my interpretation of it is objectively as valid as TPC's. There's a somewhat less objective component here as well.
The trouble with unicorns and other mythological creatures is that they don't have such clear-cut origins, often being passed down by oral folklore for generations, and often being amalgamations of a number of other different mythological creatures. I think the unicorn is a bad example for that reason, but in a case where a clear-cut historical origin can be identified, or in cases where the majority of historical accounts share the same traits, I think those interpretations can be said to be more valid than modern interpretations of such concepts.