Language doesn't obey these kinds of arguments. The non-tech world thinks wiki means Wikipedia. You can lament that, but you can't ever turn things back.
I'm talking about the opposite case, where somebody thinks "Wikipedia" means "wiki". I don't think I've ever heard anybody describe a wiki as a Wikipedia before. I don't think that's a widespread misunderstanding at all.
Regardless, language does work this way. The value of words is in their meanings. Sometimes those meanings drift, but that doesn't make that kind of drift valuable, and so it's important to resist that drift. If you make the word "wiki" ambiguous, it loses value.