You don't see Gangplank in silver because the majority of ranked players (including the majority of silver players) simply blindly play whatever they see in the LCS. "These champs are played by pros, so these champs are the best"

Now, pros don't play GP for a variety of reasons. Champs can be broken down into 4 main categories: CC, utility, damage, and mobility. He has no hard CC, mediocre utility, and a decent amount of move speed, but no dashes, no gap closers, and even if he had those, he has no lockdown to make use of the movement (see: Fiora in competitive play).

But let's say you build him pure damage. GP build for damage does indeed do a lot of damage. But there's a lot of downsides here. Huge tanks who can eat his damage who have a ton of CC, mobility, and engage potential (such as Maokai). GP is melee range, aside from his Q, but he won't be able to use his autos or his Q on any squishies providing the enemy team's frontline is doing their job correctly, which they do in competitive play. And even with these downsides, he's almost entirely physical damage, so why not play a champ who doesn't die instantly with better back line threat, like Fiora.

The best parts of his kit are The Orange, and his ult. The orange represents a way to prolong his mediocre existence, and his ult is simply so non-threatening that it is largely relegated to long-range waveclear.

Perhaps I've underspoken his utility. Perhaps the team move speed and bonus AD is better than I think it is. Janna has team move speed in a similar radius to gangplank, and while it is only while running toward her, it is passive and constant. But it's the rest of the kit that really matters. The tornado is great CC. Janna ult is fantastic peel. Or thresh for peel or engage. Or alistar for peel or engage. What's a gangplank in the support role going to do? Hit the enemy threats and yell to stop hitting his carries?

Ok, maybe not support or full damage GP. There's gotta be some tanky hybrid gangplank from either the jungle or top lane. Goes straight back to the 4 pillars of a champion. You're really going to pick GP, who's initiation involves running at you, over a top laner like Maokai, who comes with targeted, hard, very threatening CC, and is tankier to boot? Or over irelia, a tanky backline threat with a 2 second stun, resettable dashes, and arguably similar or better CC reduction...

So maybe he fits in the jungle. But you can't possibly look at me and say that gangplank does a jungler's job better than sejuani, or gragas, or reksai, or Zac, or J4... What's gangplanks gank look like? He runs at the enemy. Each of those champions have gapclosers. When gangplank catches an enemy, what's the lockdown? None. Each of those junglers has hard CC, and many have incredibly powerful ultimates.

tl;dr GP just doesn't have enough. There's better options for mobility, utility, CC, and damage, with many other champions, in every role.