tl;dr: The marginal benefits of learning a skill shouldn't be judged heavily on the performance of people who have had it for a long time. People are unfortunately susceptible to these poor judgments via the representativeness heuristic.

Warn and beware of the following kludgy argument, which I hear often and have to dispel or refine:

"Naively, learning «skill type» should help my performance in «domain». But people with «skill type» aren't significantly better at «domain», so learning it is unlikely to help me."

In the presence or absence of obvious mediating factors, skills otherwise judged as "inapplicable" might instead present low hanging fruit for improvement. But people too often toss them away using biased heuristics to continue being lazy and mentally stagnant. Here are some parallel examples to give the general idea (these are just illustrative, and might be wrong):

Weak argument: "Gamers are awkward, so learning games won't help my social skills."
Mediating factor: Lack of practice with face-to-face interaction.
Ideal: Socialite acquires moves-ahead thinking and learns about signalling to help get a great charity off the ground.

Weak argument: "Physicists aren't good at sports, so physics won't help me improve my game."
Mediating factor: Lack of exercise.
Ideal: Athlete or coach learns basic physics and tweaks training to gain a leading edge.

Weak argument: "Mathematicians aren't romantically successful, so math won't help me with dating."
Mediating factor: Aversion to unstructured environments.
Ideal: Serial dater learns basic probability to combat cognitive biases in selecting partners.

Weak argument: "Psychologists are often depressed, so learning psychology won't help me fix my problems."
Mediating factor: Time spent with unhappy people.
Ideal: College student learns basic neuropsychology and restructures study/social routine to accommodate better unconscious brain functions.

Aside from easily identifiable particular flaws [as SarahC points out, the difference between an athelete and a physicist isn't just physical activity], there are a few generic reasons why these arguments are weak:

• Having a skill and learning a skill are very different things. This is especially true when the learning is coupled with efforts to avoid compartmentalizing it. People who have the skill already might have developed it early, possibly at the cost of developing other essential skills or traits for «domain», like empathy in the example of social interaction.
• People who have the skill already probably learned it without the explicit intention to apply it to «domain». For those people, the task now analogous to learning it is decompartmentalizing it.
• People who don't have the skill already may have been busy learning other skills instead, and those may be critically helpful in applying the new skill.
• There are generalized effects like inspiration, mental refreshment, and adaptive attitude that come from learning just about anything new as an adult.

All this should be taken into account before dismissing the new skill option. In general, try to flesh out the analysis with the following themes:

• Synergistic marginal effects – If your other existing skills differ greatly from the relevant specialists', the new skill may have marginal effects that it wouldn't have had for them.
• Compartmentalization effects – There may be obvious reasons to suspect the specialists are compartmentalizing their skill.
• Learning order effects – Contrary to popular belief, some skills are more productively learnt as an adult: growing up sometimes makes excellent background material.

So yeah, don't let specialists over-represent the skills the specialize in. Many readers here are in the "already have it" category for a lot of the skills I'm talking about, and there are already lots of posts convincing us to decompartmentalize those skills… but it's also helpful to consider the above ideas in balance with the legitimate counterarguments when convincing others to learn and apply new skills.