Doesn't that just run into the problem of making items boring stat sticks that over-value %increases to the stats that they give?
It does if it's poorly implemented.
I don't have a problem with items having actives and passives, they should just be weaker and secondary to the stats that they give. I have issues with items like QSS and Zhonya's because of this, I think that they fall too far into the grounds of hard countering picks with items, which is not something I'm a fan of. I don't mind actives and passives though, Randuin's for example has a fair active, it's strong but not insane and a passive that adds to the overall direction of what the item is meant to do.
The problem is that League is a game of mad snowball potential
Yes it is. The solution is to add anti-snowball mechanics to the game and cripple some of the worst offenders cough Lee Sin cough.
And that's before we consider League's static itemization problem for carries which doesn't let them adjust to the status of the game because they simply don't have the option
League has reactive stats. You can reactivity buy armour and MR. Almost every champion can work out a way to utilise a cloth armour or a null magic mantle.
The problem is that Riot caters to the idea of a 6 offensive item carry. This never used to be a thing. You used to see carries build items like Merc Treads, GA and even Randuin's. Going 6 offensive items on a carry used to be the stupidest thing you could do. There was a point where a carry had enough damage and just needed bulk to ensure that they couldn't be burst.
When this was the case it wasn't that painful to drop 700ish gold into a Chain Vest, you were eventually going to need a GA anyway, if it lets you stay in lane why wouldn't you?
but in League the late-game carry items are inexplicably also the most efficient for them
This is actually untrue right now, people just haven't caught on yet. Component items are currently the most efficient for their cost. The best snowballing ADC build is BF>Zeal>BF>Pickaxe. Still this doesn't really fix issues, because if you're behind the other guy will probably go for this build as well if it ever becomes popularised.
That's a comfortable thing for me to know that some FotM pick can't just steamroll our team just because they're a little strong right now since good counters exist to keep them in check even when they're comparatively crazy.
I'm not afraid of FotM in League, I'm more worried when my team picks it. Most FotM players have no idea what they're doing and are utter nonissues. What worries me is when I see a champ like Singed, because I know there's a good chance that whoever's playing him knows exactly what he's doing.