There are two aspects to what you're describing and I am not sure you can combine them in the same idiom.
- You say
someone who understands their audience perfectly and always says exactly what needs to be said when it needs to be said.
That's the definition of being to the point:
expressing something very important or suitable for the subject being discussed:
- Her comments on my work were very apt and to the point. (Cambridge)
Free dictionary elaborates a bit more:
- Relevant, concerning the matter at hand, as in
- Her remarks were brief and to the point [Early 1800s] For an antonym, see beside the point.
- Concerning the important or essential issue. This usage is often put as come or get to
the point , meaning address the important issue. For example,
come to the point; we haven't much time, or
- Do you suppose he'll ever
get to the point of all this? [Late 1300s]
- But the quality of character of getting straight to the point is pretty well expressed by a phrase you use:
get/cut to the heart of the matter or cut to the crux of the matter
The essential point or problem is the crux. People are always trying
to get to the crux of a matter or the crux of a problem, while others
try to distract them.
The noun crux is often followed by the phrases "of the matter" or "of
the problem." When people are trying to identify the crux of
something, it's like they want to get to the heart of it. They want to
peel back the layers and find out what something is really all about
or what is causing the problem. No more beating around the bush! (Vocabulary)
Crux is defined by Cambridge
the most important or serious part of a matter, problem, or argument.
Other variants include: Get to the nub of the matter, or get down to the nuts and bolts