i like how you've framed the goal as stakeholder capture. And I agree designers have an advantage.
The rub is stakeholders are people. I'd bet on learning the skills for earning trust from a person (including charm) over a particular method or tool. I want the stakeholder to say "I trust the ideas from <insert designers name here> over the rest of the team, even though theirs take more time, because they are right far more often than the rest of you." That's it. It's a reputation game. Tools can help earn reputation but trust is far more nuanced than mastery of a low-fidelity idea communication skill.
Winning that reputation usually takes a few cycles with stakeholders picking the fastest gun and seeing the consequences. That's when they are ready to hear the argument that what they really need is the fastest gun *with good ideas* - since it's far more valuable.