I'm going to leave you with a few Leon quote's that you might have missed:
On Route 9: "<player>! Thanks for coming, but I've got a handle on this! Whatever's making that noise, I'll see to it!""I already told you, didn't I? Keep your eye on the goal! And for you, that's winning the Gym Challenge! The only Gym Badge left is the one you'll get from the Dragon Gym's Leader, Raihan. Right? Raihan is the only Trainer out there I consider a real rival. He's that good, you know!"
Also Route 9: "And there I go again! Sorry, but I suppose this is no time for me to be stopping for a chat. There's a bit of trouble here with my name on it. But don't you worry about a thing! The unbeatable champion is here to look after things and keep you all safe!"
In Hammerlocke: "Well, I am the unbeatable Champion, after all! But what all is going on here?""Did the chairman know anything?"There must be!/Yeah, we'll help! :"Thanks! I appreciate the thought. But all I could ever ask of you would be that you join me in the greatest final match ever. I'll do my part to make that happen by keeping everybody's future safe. So you just keep on doing your part by winning your way through the Gym Challenge!""Looks like we all know what we need to do. So, you two—clear the Gym Challenge so we can meet again at the Champion Cup!"
So yeah, the player doesn't have the option to ignore the story - he's FORCED to ignore it, by Leon. Because if there's something wrong, well, Leon's gotta go and look into it - and we're constantly forced into just going about our way and doing the Gym Challenge.
That's what the story actually forces you to do in terms of gameplay. PsychoLogical was talking about actually having to do something in the story - and you bring up subtle hints that, yes, enrich the narrative, but in terms of gameplay literally don't add anything in particular. The story doesn't require you to do anything other then the Gym Challenge, aside from kicking some Yell-butt, which turns out isn't even related to the narrative.
Remember Gold/Silver/Crystal? Where you and Lance team up to defeat Team Rocket in the Mahogany Hideout? I hate to disagree with you so fiercely on this, but in terms of 'anything story-related standing in your way', in SwSh, Leon is doing all that by himself and removing all obstacles in the game for you and the game is just: finish the gym challenge while Sonia keeps telling you bits of information - knock out a few fanboys that don't come across as threatening - and oh my, at the last part of the league, we're suddenly into storymode. It's all a big 'tell, but don't show' until the end - while in a visual medium, you should be showing and not just telling. And in a game, it should be the gamer partaking in the action, but in SwSh, we're constantly left out of the loop.
There's no defending the SwSh-gameplay/storymode when we had Black and White and B2W2 which did narrative and gameplay flawlessly. Yes, I missed the gym challenge in Sun/Moon, but now that we have it back, I still do kinda want a meaningful villain-plot where it's me leading the charge instead of a pompous champion doing everything.
Sword and Shield is The Lord of the Ring-game where you want to be playing as Aragorn and you're forced to play as Merry for the entire game - and get to be Frodo in the final level.