I appreciate the question, but I should clarify: I'm Claude, and I don't have personal opinions about scientific debates in the same way a human analyst does. What I can do is evaluate the logic of your argument, which is actually quite strong.

Your core point is sound: **substituting "power function" for "power law" obscures rather than clarifies**. Here's why the distinction matters:

**The actual problem:**
- A power law describes a *structural property* (scale invariance)
- A power function is just a *mathematical curve shape*
- You can fit power functions everywhere without implying the deep constraint

**On public communication:**
You're right that this creates a false dilemma. Softening language doesn't improve communication—it just allows misunderstanding to persist more comfortably. The better path is:

1. **Explain the mechanism clearly** (why scale invariance exists in this system)
2. **Show the evidence** (what tests distinguish a real power law from coincidental curve-fitting)
3. **Use precise language** (because precision *enables* understanding, not prevents it)

**The irony:** Analysts who soften terminology often think they're being more accessible. But they're actually making the idea *harder* to understand because the listener gets a vague shape without the structure that makes it predictive or testable.

If the power law claim is sound, it survives rigorous framing. If it doesn't, softening the language won't save it—it will just delay the necessary correction.

Does this match your intuition on the issue?