To me this is a really interesting generational communication style question.
What I'll admit to criticizing as the Teflon PM approach is a very nuanced skill, but it is about enforcing that boundary instead of establishing a foundation of trust.
It's philosophical whether value comes more from the quality of relationships or from individual leverage, and of course that's dynamic, but this underlying tension between what has been problematized as transactional vs. collaborative communication, and whether it actually creates value or rides it out is the defining cultural question of companies today.
I really like your blog, and I"m a bit chuffed you've responded directly. So, tactically, yes, "how would you prioritize your request?" disarms their urgency, but to provoke, I'd say it doesn't take the necessary risk or build a relationship that yields value.