Corki has pretty much always been a dominant ADC.
There was a short period of time in season 3 when he fell out of favor (a lot out of favor actually), but then Tri-Force got re-worked and he wound up being the #2 ADC for most of the competitive world's scene.
Bigger picture problem with Corki and Lucian seems to be the early-game push of champions in competitive play in general. More often than not the pros seem to favor lane-dominance or a strong mid-game, favoring momentum plays capable of swinging a game earlier rather than later. If you close out a game at 33 minutes due to setting a 40 minute team back 10 minutes and crushing them - they never get the opportunity to turn around 50 minutes in and swing it back.
Game's already over, which is why champions like Poppy and Tryndamere are hardly ever played competitively.
Ezreal was a major mid-game marksman as well, having similar burst and mobility to Lucian and Corki.
To complicate things further - late-game marksman like Tristana and Kog'Maw only really saw the light when the player base at large felt overwhelmed by their power, then those champions proceeded to get exploited for their late-game reliance by SSWhite in a string of near-perfect sub-30 minute wins.
So - seems like kind of a mess.
Big issues item-wise is that defensive items like Randuin's Omen, Thornmail, Warden's Mail, Doran's Shield, Ninja Tabi, Frozen Heart, and more have near useless passives vs. ability-reliant, caster-heavy marksman like Corki and Lucian.
Other big item issue is that Infinity Edge and critical strikes late-game get a little out of hand. Not unbalanced in the grand scheme of early/late, but powerful enough to tip champions like Tryndamere and, with his current nerfs, Yasou, so far down early-game they become a major risk and struggle to even bring into late.