I understand your point, but I am not sure a new term wouldn't have been co-opted (if it was any good). It would certainly have hurt adoption (if it was not as good).
I also like the current terminology better tbh ("open", "available").
If they had invented a new term, then they could have obtained a trademark for that term, which would properly allow them to enforce their definition and ability to certify licenses as open source. That's usually how this works, for example POSIX is a trademark of the IEEE. (the other possible route is enforcement/certification by a government agency, for example organic food must meet certain farming practices to be called "organic".)
Instead we have a situation where they didn't invent the term but they lie about it and said they did. They don't have a trademark and obviously aren't a government agency, so enforcement is left to random people acting as self-appointed terminology police on their behalf. And then we get huge subthreads like this one, where a bunch of people have to argue about whether one of the most successful open source projects in history is really even "open source" :)
I also like the current terminology better tbh ("open", "available").