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Much of League is about converting gold into power. This question concerns whether different Champions have different conversion rates. The conventional wisdom that I received "back in the day" was that ADCs convert gold into power much more impressively (for large values of gold) than, say, fighters or mages. This was the best justification for "not KSing" that I heard—if we assume that 300 gold does more for Ashe than it does for Janna, you want that kill going to Ashe if possible. It was also the justification for supports warding—once a ward is placed, it doesn't really matter who placed it, it gives power independent of the Champion. Therefore, you might as well have the Champions who gain the least from stat-boosting items buy the wards.

Linear warriors, quadratic wizards

There's a tabletop saying: "linear warriors, quadratic wizards". In other words, some classes follow a fairly linear strength progression, whereas others start out super weak and then ramp up out of control. As a friend of mine once put it, this explains why hiring mages in D&D is a bad idea: the kind of mages you can afford to hire are useless ("COLOR SPRAY! COLOR SPRAY!"), while the mages you want to hire are ascended demigods who "have no need for your pitiful mortal currency".

Cubic carries

When I was introduced to League, it was explained to me that League followed this principle, but added a third category: in League, it was "linear fighters, quadratic mages, cubic carries". Back in the day, "carry" always meant ADC; the term "AP carry" would have been received as a contradiction in terms. Some later added "constant supports".

The explanation for this theory was largely stat-based.

• Supports have lots of base utility (a level 1 Blitzcrank with no items can still grab a level 18 fully-fed enemy), and sometimes base damage (old Sona's power chords). This was even more important before the Support gold changes: supports were Champions who could thrive on little or no farm. But to keep them balanced, they don't scale well.
• Fighters scale mostly on things like attack damage, health, and resistances, which don't directly reinforce each other.
• Mages scale on at least two main stats, AP and MPen, that synergize with each other, producing a quadratic effect.
• Carries (i.e. ADCs) use autoattacks that scale on multiple stats that directly multiply each other—attack damage, attack speed, crit, ArPen—and thus follow a cubic or higher power-vs-gold progression.

But Riot also was allegedly trying to break away from the DOTA tradition of "hard carries" who, if fed, could legitimately 1v5 the enemy team, and gives mages more late-game potential. In the past few years, people have even begun speaking of "AP carries".

My question

So what do you all think? Has Riot discarded this model? I've noticed a couple trends that suggest it has. For example, supports often scale better with gold now, and a lot of "ADCs" are really "AD mages", with tons of (AD-driven) abilities.