I am wondering this because Riot has put an attack speed cap on for a reason (BORK + vayne passive = byebye), but there is no AD cap... this makes me think that AS could hypothetically be more powerful than AD contingent on the scenario in which there were no AS cap.
That's really not the case.
With an ADC build, if you start with 100 AD and 0.666 attacks per second with +50% AS from leveling (or 1 attack per second), then:
- getting 150% AS will double your DPS from 100 to 200.
- Getting another 150% AS will increase your DPS from 200 to 300, or a 50% increase.
- Getting another 150% AS will increase your DPS from 300 to 400, or a 33.33% increase.
- Getting an additional 150% AS will increase your DPS from 400 to 500, or a 25% increase.
- Getting an additional 150% AS will increase your DPS from 500 to 600, or a 20% increase.
Alternatively:
- Getting 100 AD will double your AA DPS from 100 to 200 (often along with increasing your QWER damage by a solid margin)
- Getting 150% AS will then double your AA DPS from 200 to 400.
- Getting 66.67% crit with IE's passive will then further double your AA DPS from 400 to 800.
- Getting 50%+50 armor penetration will then cause your effective DPS vs. anyone with 100 or more armor to double, the equivalent of going from 800 DPS to 1600 DPS.
- Provided Hurricane's side bolts could critically strike, getting Hurricane at this point would cause your DPS to move from 1600 to 3200 (but they can't, for reasons which should be pretty obvious at this point).
With AP itemization and defensive itemization there's a similar pattern. Going ham by perusing a singular stat and you're late game will suffer immensely, as you're linear scaling pursuit will often be crushed by the exponential scaling of your rivals. Only a few stats stack exponentially with themselves.
One of those is CDR, as 80% to 90% CDR isn't a 10% boost, you'r cooldowns go from 20% to 10% of their original length with only 10% more, causing that last 10% to do everything the first 80% accomplished: hence the cap at 40%/45% to prevent the stat from getting extremely out of hand (though why CDR is set up in this way when armor, MR, and AS all scale linearly as % stats is a bit beyond me, it's entirely possible to set up CDR where infinite CDR stacked values could be balanced rather than having 100 offer infinite DPS, or rather DPS only limited by casting times or the game's capacity to detect a click in the case of skills with no animations).
But anyways: the AS cap mostly prevents bad players from making poor build decisions. Nobody scales well enough with %AS alone to cover a 500 vs. 1,600+ discrepancy.
I am wondering this because Riot has put an attack speed cap on for a reason
The reason is purely aesthetic as far as I can tell.
At it's heart LoL is based off of the popular Warcraft III custom map: DotA.
And with playing a lot of custom WC3 maps, allowing champions to constantly scale AS makes them look derppy as heck while they're spassing out with that 1,000%+ AS. It looks hilarious but also pretty unclean, especially seeing as animations feeling right for slow attacks look very different than animations feeling right for fast attacks.
You could compare 
vs. 
for this. Yasou actually holds his sword still after swinging for a good portion of his AA animation, allowing him to strike some cool and memorable poses that look solid with high %AS values, where Garen's sword swings emphasize it's weight and cause him to swing left for one attack and then right for the next, matching a cooler aesthetic for low %AS values but looking a bit wiggly-noodly with lots of %AS.
If there wasn't an Attack Speed cap... What would be the max AS?
Answer can be found by looking at LoL Wiki and typing in AS, then picking the champion with the biggest combination of base AS+AS steroid, finding 4 champions that can give %AS buffs, finding any jungle camps/global map properties that potentially increase AS, finding if any items offer a passive that boosts %AS higher than the passive %AS provided by the best %AS items, then filling a build with as much stacking %AS as possible.
Probably in the neighborhood of ~700%.
Or for 3 auto-attacks or less 
, seeing as 1 of his skills causes him to fire 3 shoots as fast as the game allows, which would be infinity fast with no %AS limit.
