I don't think that's merely an irrational compulsion. Communication can immediately demonstrate intelligence, and I think it quite clearly has, in numerous ways. The benchmarks out there cover a reasonable range of measurements that aren't subjective, and there's clear yes-or-no answers to whether the communication is showing real ways to solve problems (e.g. change a tire, write lines of code, solving word problems, critiquing essays), where the output proves it in the first instance.
Where there's an open question is in whether you're commingling the notion of intelligence with consciousness, or identifying intelligence with AGI, or with "human like" uniqueness, or some other special ingredient. I think your warning is important and valid in many contexts (people tend to get carried away when discussing plant "intelligence", and earlier versions of "AI" like Eliza were not the real deal, and Sophia the robot "granted citizenship" was a joke).
But this is not a case, I think where it's a matter of intuitions leading us astray.