Just going off a bunch of things that people have said in this thread (and others) as well as my own thoughts.
Gangplank is... not particularly a healthy champion in my opinion. He has wave clear, a substantial AOE slow, consistent gold generation, global pressure, zoning, and damage, a very good duel and skirmish performance, a short cooldown cleanse and heal, and a resetting mobility and true damage passive. Really the only thing he doesn't do well is hard CC, though he does have significant slows, and fights where he can't set up before hand.
You can't really say that you 'beat a champion early' and they become useless because that's frankly not true. Beating a champion early means you set them behind while you go elsewhere to try and do other things. That lets them farm back up and get back into the game and usually unless you end the game very early, beating a champion early isn't really going to help you late game. Not to mention that relies on at LEAST four players; you, the Gangplank, and both teams' junglers. To successfully put an enemy behind, you must capitalize on their missteps and be aggressive within your champion's abilities and your jungler must also be there whenever the enemy jungler tries to gank. That's far easier said than done even in the best of situations, but I'll get to Gangplank specifically in a little bit.
Sure, he does not have a particularly strong early game until he gets a couple components and levels under his belt, but that doesn't change the fact that he can push very heavily, push down towers effectively, poke rather safely, and if the player knows generally what they are doing, constantly harass and zone you. His Q is on a 5 second cooldown at all ranks (which is effectively the same cooldown as a max-rank Nasus Q without CDR.) and he will generally have 20% or more reduction on his timers from what I've seen.
For people who say that you walk out of his barrels or pop them before he can to counter him, that really isn't an option much of the time when facing a player who has some understanding of the champion. For basically guaranteed damage, a Gangplank will prepare a barrel behind him and then walk past it so it is less contested to be destroyed. When he shoots it with his Q, he will drop down two or even three barrels in less than a second in the middle of the animation to give enemies almost no time to react. It is simply not possible to attack a barrel three times the instant it is placed unless three players on your team with decent attack speed target the barrel as soon as he places it because then their focus is not on the fight. Barrels will also become untargetable and unkillable about... I'd say halfway through the fuse line between two barrels. At this point, you MUST dodge the blast radius to avoid damage, and that is quite difficult without a dash or blink and very fast reaction times. The radius is large enough that you cannot simply walk out of it if the Gangplank drops the target barrel right next to you if he chains properly.
With his barrels resetting his passive, Gangplank can very swiftly push towers early if you leave to roam and even then, he can contribute from across the map with his ultimate, so roaming isn't consistently efficient counter to him.... So what is?
The only real counter to Gangplank is the same way you'd deal with an Illaoi or a Teemo. Don't go to him to fight, take him where his barrels aren't and then you have to burst him before he can let one of his barrels tick down. That means, after level 13, you have one solitary second to chunk him before he can explode a barrel, and thereby chain explosions on to you. Of course his Q and W both have cast times, but the amount is negligible in the grand scheme of things. Speaking of his W, it is a cleanse and a heal on about an 8 second cooldown at max rank with 40% CDR that scales with missing health. Unless you baited out his oranges within the last 10 seconds, he becomes that much more difficult to lock down and burst.
The problems, in my eyes, is that he is overloaded with so much versatility that he is hard to deal with, but to get a better understanding, let me break down each ability concisely.
Q-- It's a spammy, relatively cheap spell, in the same vein as an Ezreal Q. It gives him some targeted range and medium damage without a crit. However, it gives him gold generation that he really doesn't need. I get that it fits with his theme of being a pirate, but he already gets his Silver Serpents for that. The extra gold just puts him automatically ahead of everyone else just for CSing.
W-- It's a near-instant cleanse that will release him from every crowd control effect except for displacements that also heals him. On how short a cooldown it can easily be, I think the spell is frankly broken.
E-- These are his big damage source. Long range zone, poke, waveclear, and farming on a short cooldown and they ignore 40% of your armor, so unless you build full armor, he'll still chunk you with a barrel planted next to you and exploding an instant later.
R-- My only complaint about this spell is that it is global. For something so tide-turning in a fight, I think it really has to have a set range like Ziggs' R or Pantheon or Twisted Fate or Nocturne. They all have long range, impactful ulltimates, but they are not global like his is. It just gives him too much freedom to farm in top lane while the rest of his team fights for bot lane inner turret.
If I had the opportunity to personally tune Gangplank, this is what I'd do.
Passive-- This can stay the same. I think that it is fine when taken with the other changes I would make.
Q-- Lower the crit damage like with Yasuo. The fact that he is melee and his ranged poke can crit for full damage, even with his barrels, make it too powerful for the short cooldown. Another, possibly simultaneous, option would be to remove or simply halve his gold generation passive. Prevent him from snowballing out of control against his laner simply from farming.
W-- As much as I hate this spell when it saves him from death at the last moment, all I think this needs is maybe a 5 mana cost increase across the board and one major change. Make it like Evelynn's W where it only removes slows and nothing else. I could understand removing snares as well, but please, don't let him cleanse out of stuns and suppressions for free.
E-- His barrels absolutely need to have a mana cost, just like Teemo's R or Heimerdinger's Q. I'm glad that they rely on stocks as well, but he cannot be allowed to plop them down for free to chain away to his heart's content. It affords him too much safety and zone potential. In addition, allowed the splash damage to crit ON TOP OF the 40% armor penetration is just silly. One or the other, please. Another thing that would be an option would be to give his barrels an arm time where they can still be damaged, but they will not blow up. That would allow counterplay in that he cannot drop a barrel on your face while two more are going through the explosion animation and exploding the one beside you before you can even path away from it. It doesn't have to arm for as long as Jhin's traps necessarily, but it would be a lot less frustrating if he was no longer able to hit you with a huge burst of damage for no mana from long range, even from a bush, with no possible reaction unless you have a blink or dash to escape.
R-- Honestly, this is in a good place if it were given a set range that he could cast it from.
These changes would force Gangplank to use his barrels more strategic, but it would make Gangplank more of a participant in fights in the same manner as a Ziggs where that he can get close enough to throw out an ult and then go back to farming if his team doesn't need him, or he can get in to the thick of it and use his AOE and chase potential to aid his team.
I will not confess to playing a lot of Gangplank or being particularly mechanically skilled, but I would like to think that I am decent at theory crafting and I would love to know what the rest of the community thinks.
Lastly, if you got to the bottom of this monster of a post, thanks for reading! Have a wonderful day.