Okay, this is intended to fix a (possibly perceived) problem with melee in SR4/5. If you want to build an elven knifemaster kind of build, Strength is your go to stat, even if you're using the knife as a precision tool. Moreover, all but the heaviest melee weapons are useless to low strength characters, and even then are of dubious utility (a combat axe at Strength 2 gets outdamaged by an Ares Predator) so while it might make sense in real life to carry a combat knife as a backup, in SR it makes no sense, unless you're a melee build to begin with.

Finesse weapons are small swords, knives and anything else that's more about hitting the right place than hitting like a truck. So no combat axes or claymores. Generally anything that outdamages a katana isn't finesse. Finesse weapons can use either Agility or Strength to determine damage, whichever is higher. So a Nocturnal Blademaster (Augmented Agility 10, Strength 2) deals 12P (Agi+2P, SR5) with a combat knife, for instance, while only dealing 7P damage with a combat axe (Str+5P).

This means elves, gnomes and other agile yet weak metatypes can be melee builds, when previously an unaugmented troll with a kitchen knife would outdamage them.

This wasn't already a rule? I may only played DnD but it just seemed common sense in general to have a finesse rule of some sort.

If you think it's necessary and balanced, knock yourself out.

One of those lessons man learned in the late middle ages.

The gun is more powerful than the sword.

By all means change it if you think it suits your game, but be aware that with Agility linked to both firearms and melee, you're making it a lot cheaper for a sam to be really, really good in a broader set of abilities.

If you want to do it, do it. However the whole hitting them in the right place thing is covered by Agility being used in the attack test, generating more hits...

This.

While I agree with the overall idea that edged weapons requires less strength, especially the cutting, stabbing and slicing ones, Agility is already king because it's used to hit. The troll with Str 10 and Ag 3 hits like a brick, but seldom hits. The elf with Ag 10 and Str 3 hits often, and with a katana 6P+net hits isn't too bad, especially with AP.
If you really want to go combat knife all the way, pick an adept and get up to 6 more damage because Magic.

Besides for what has already been said by the other commentators, strength always matters for hand to hand combat. The idea that someone could be agile but weak, and still a top tier combatant, is basically a fantasy. The best combative sport athletes are both strong and agile.

Aren't trolls screwed over enough already, without taking one of their few strong areas away from them? And isn't Agility already the super-stat? This rule would unbalance the game towards high-Agility characters, who already get extra hits (and thus extra damage) from their higher dice pools.

Not balanced at all - but not every house rule needs to be. If your campaign is all players with nimble elves complaining about their low base damage codes, and trolls are only NPC opposition or cannon fodder, then that's fine.

at least in SR4, the other aspect of damage output is calling shots or whatnot - for melee weapons,

A knife is a backup emergency weapon, or a stealth weapon. If you run out of ammo, you can at least kill your target (otherwise you have ot knock them out first, then kill them, if you are aiming for that).

Even with a sliencer, there is risk of a gun being heard if you take someone out. a knife is otherwise silent, barring the actual attempt if it goes wrong.

Still, the game is aimed a bit more towards guns. That may be on purpose, so adepts can glory in the enhanced weaponry field.

So much so that they broke down Quickness from earlier editions into Ag and Re to try to make it less of a God-stat.