Attribute Boost (STR) doesn't make you stronger, it boosts your ability to perform feats of Strength.
For example, it doesn't increase the amount you can carry (derived stat based on attributes), but it does improve your ability to lift heavy objects (Lift/Carry Attribute Test)
By a similar metric, boosting Agility would improve your ability to jump (better dicepool), but would not alter the limits for maximum jumping distances, which are derived values based on Agility.
Damage is not a dicepool, it is a derived value based on Strength. I'm sure there is a common houserule that people use for letting Attribute Boost (Strength) increase melee damage, but the OP is correct, it isn't RAW. And as far as I recall, there haven't been any responses to this topic previously to indicate that the author's intent was to have it the other way either.
I'm putting in Kiir, if agility adds to attack pool, which it does, then agi adds to damage. Thus strength should add to damage as well. Otherwise the power makes no sense.
In all the years i have played SR I don't think i ever even seen a feat of strength rolled, let alone rolled one. So a power that only adds weight lift is totally useless. You wanna lift something in SR? Go get a hydraulic jack and go lift it like ya mean it, if you want feats of strength go play Exalted or Super hero game. There we see some feats of strength rolled. How many times has anyone seen a feat of strength rolled in SR?
Damage isn't derived it has no other attributed added, and it sure as heck isn't listed derived stat section. So that's clearly wrong Kiir. Melee damage comes from strengths, it's what attribute primary value is.
As to your point Reaver I don't buy it ether, the purpose of the power is boost the attribute, down side have put up with drain. Sure it won't effect Limit, that's fine, no wants to recalculate limit constantly and Initiative has power to does that already. But Reaction adds to to dodge or driving pools, agi adds to hitting. Body adds to soak, but strength is just SOL for no reason? That logic makes no sense to me. I'll call BS on it every time.
We can find out what is intended just by submitting it. If comes back y'alls way then the power's name should be errata-ed to make it, boost ever attribute but strength. B/C it will have zero value in systematic terms, and I think that would just a terrible waste for everyone.