Yes it does and it also seems to be the point.
Strength is the only attribute that "double dips" in the sense that it provides more than a dice pool bonus to tests. (Ignoring limits for a moment) The only conceivable reason why the power would specifically state dice pools is to ensure the boost does not affect limits and secondary derived stats, such as melee damage.
Strength based weaponry is already very troublesome due to how high strength can get. Even a human can get up to strength 10 with relative ease, which makes a throwing knife equal to an assault rifle in terms of damage. It absolutely does not need to go further with adept powers.
Counterpoint: there's
two Strength skills. Two. Somehow I doubt it was intended for Boost Strength to be a drain granting, crappier version of the improved skill power. Also, strength based weaponry is troublesome for the opposite reason - a human cannot get strength 10 with "relative ease," because that costs a
lot or resources. It is in fact the literal opposite of "with relative ease." If you're an adept, you essentially cannot get strength 10 at all - which is stupid as hell, because adepts were always
the "melee kung fu" dudes, and now they suck at it. Lastly, it cannot "go further with adept powers." methods of increasing attributes don't stack. Ten is the cap for a human - period, forever, the end.
Also I'm not sure you can really say strength is the only skill that "double dips." Agility provides movement and, like, nearly all the important skills in a fight. Reaction and Intuition provide initiative and defense rolls. Body and Will add health boxes. Will, Logic, and Charisma potentially add to drain soak. Logic is used to defend for a high number of spells.
So not only is Strength
not the only one that double dips, it is, along with charisma, one of two stats that most runners will
never use, ever. The only reason to stack strength is 1) melee damage, and 2) physical limit. And Boost Strength doesn't help either of those.
...In fact I'm pretty sure almost everything you said is the opposite of reality.