>Imagine all of the people who have been arbitrarily labelled as "alt-right" in social and traditional media. Do you actually think this is what they generally want?

Many of them self identify as alt-right. It's largely a self-selected identity. They're often proud of the term too. I have yet to see someone mislabeled alt-right when they're a vanilla conservative. Alt-right really is the far right of old but with Gen Z aesthetics.