Isn't it the opposite? People who are willing to say that a simple ELIZA bot is a form of AI think that something being AI isn't very important; it's a low bar to clear and doesn't imply much about the usefulness of the thing. To these people, AI is not intrinsically important. A chess bot is AI, it has very limited utility and just isn't important at all in any domain other than chess.
On the other hand, people who say that AI is an as-of-yet unobtained far-future technology are saying that AI is intrinsically very sophisticated and useful; so much so that nobody has succeeded in creating one yet. These people think that AI is intrinsically important. They think the term AI is so important that it must not be applied to systems with limited mundane usefulness.
> They think the term AI is so important that it must not be applied to systems with limited mundane usefulness
Yes? Thinking is hard. People would happily delegate as much cognitive load to a computer as possible - especially if they believe the computer is intelligent. With this comes 'computer says no' and 'we are not responsible; it was the AI that was behaving unjust'. Until we have an artificial intelligence that can take responsibility for its actions - and remedy them if needs be, we should hammer home that these systems have limited mundane usefulness.
People delegate their decision making to other systems all the time, whether or not those systems are termed to be AI.
There is no empirical test for whether or not a system is AGI, and 'AI' is a term which has been applied to all manner of mundane systems for decades already. It is not important that we restrict the term AI to only mean AGI (whatever it is that AGI even means!) The 'CPU' players in Mario Kart 64 were frequently called AI, and there was no problem with that. Anybody who gets bent out of shape over the casual use of the term AI is placing way too much importance on the term.
On the other hand, people who say that AI is an as-of-yet unobtained far-future technology are saying that AI is intrinsically very sophisticated and useful; so much so that nobody has succeeded in creating one yet. These people think that AI is intrinsically important. They think the term AI is so important that it must not be applied to systems with limited mundane usefulness.