Does anyone know of an in-universe explanation for why you need Gym Badges to use HM moves outside of battle?

[Red Knight]

From a Doylist perspective, the reasoning is pretty obvious: it's a method of gating off progress. For instance, in RBY they didn't want people getting too far away from Cerulean before they beat Misty, so they gated off Rock Tunnel (and by extension all of Kanto except the areas immediately around Cerulean and Vermilion since Saffron is closed off and Snorlax blocks off Route 11) and Surge's gym behind Cut trees and made it so you need to beat Misty to use Cut outside of battle. Or how in Johto, Hoenn, and Sinnoh, you can't even reach Victory Road and the Pokémon League without Waterfall, which you can't use without the Rising/Rain/Beacon Badge; likewise with needing the Earth Badge to use Rock Climb to scale Mt. Silver to reach Red in HGSS.
But what is the Watsonian reason? Why are people unable or forbidden to use HM moves for traversal without gym badges? I've been playing through Alpha Sapphire and multiple NPC's have referred to needing gym badges to use certain HM moves (for instance, a Fisher on Route 128 near the base of the waterfall that leads to Evergrande says, "Awww, phooey! My Pokémon knows Waterfall, but I don't have the Sootopolis Gym Badge!"), but I don't recall any of them ever giving a reason why they need the appropriate gym badge.
I have two theories. One is that there is some kind of legal restriction on using HM moves without the appropriate badges. But the Pokémon world has very few centralized authorities capable of enforcing such policies. Sure, a Pokémon League organization might have the authority to regulate the actions of Trainers in its region, but they hardly seem to have the resources to go after Trainers who don't abide by these restrictions. Also, what would be the purpose of such restrictions? Many HM moves are needed to traverse the landscape of the region, and none of the regions where using HM moves outside of battle requires a badge have robust public transit (the only things I can think of are the Magnet Train that connects Goldenrod and Saffron and a couple of ferry services, like the Seagallop ships that take you around the Sevii Islands in FRLG and possibly the SS Tidal in Hoenn, which only goes between Slateport, Lilycove, and the Battle Frontier; Mr. Briney is not public transit, as he's ferrying you around at President Stone's behest and as a personal favor for saving Peeko). So these regulations would end up unfairly screwing over a lot of people who live in remote towns like Cinnabar, Cianwood, Blackthorn, Dewford, Mossdeep, Sootopolis, Pacifidlog, Canalave, Snowpoint, etc., who could otherwise use Pokémon with HM moves like Surf and Fly to navigate their regions - especially since most of the time the badges you would need to use those HM moves are not related to those remote places (the only exceptions being Cianwood's badge letting you Fly and maybe Snowpoint's badge letting you use Rock Climb). And this level of systemic injustice seems rather uncharacteristic of the world of Pokémon to me.
The other theory is that it's similar to how disobedience works; your Pokémon don't trust you enough to do the things until you prove your worthiness to them. But this has its own holes. For instance, if you have a Blastoise or something that already trusts you to handle it in battle, why would it not also trust you to guide it as it carries you over the water until you further prove your worthiness in battle?
IDK, it seems like the devs didn't really think through the in-universe justification very well. Which is fair when your main objective is to make an enjoyable game that isn't frustrating or overwhelming to play, which is what the badge restrictions are intended to help with. But it is still somewhat disappointing.

 

[Zexy]

Before ORAS, my headcanon for this was that it just never really happened from an in-universe perspective because the player Trainer just challenges Gyms the first moment they are available. It takes some severe sequence breaking from us (who know what happens next) to actually do SS Anne before Misty... But our player does not actually know this is possible in-universe and just keeps challenging Misty in Cerulean and maybe training if they fail, until they succeed.

In fact, before I actually found Bulbapedia and read up on these things, I have never even once been in a situation like this as a kid. It happening is not supposed to be natural in universe progression.

ORAS was... A breakthrough when it comes to Watsonian-Doylist integration. Zinnia confirmed multiple universes exist, some with Mega, some without... Link Cable is a device that connects universes, implying that every save file ever is its own universe. But for some reason, in these particular universes of the ORAS cluster within the multiverse, this info became more commonplace, maybe to the Draconids, but eventually to other people too. Such as the NPC for the Waterfall in Ever Grande, or even worse, the Route 121 one that says you can only Fly here after reaching Lilycove, which is something no kind of offiicial legislation could reasonably account for. It is as if people here kinda know they live in a simulation.

Thankfully we just got rid of HMs starting with Gen 7, so all is well now.

 

[Red Knight]

...or even worse, the Route 121 one that says you can only Fly here after reaching Lilycove, which is something no kind of offiicial legislation could reasonably account for.

Indeed. From a gameplay standpoint, yes, you can only Fly to certain routes after you've been to a nearby town. I guess the Watsonian justification is "you (the player character) need to have been to a place to understand how to guide your Flying Pokémon there or to the nearby areas, using cities and other major landmarks to help you find where to land on routes." But then there's soaring on Lati@s by using the Eon Flute, which lets you fly to Mirage Spots. Then again, aside from Mirage Spots you still can't land in places you haven't been (e.g. you still can't land in Pacifidlog if you haven't already been there) so I suppose you could say the ability to find and land in Mirage Spots is a unique ability of Lati@s. But the way that NPC on Route 121 phrases it is way too vague to directly imply this. It's just, "go to Lilycove so you can Fly here later!" or "Oh! You can Fly here! I'm going to visit more towns so I can use Fly to reach more places!"

 

[Rachael]

Of course, this isn't a perfect answer, but my guess is that they work sort of like the barriers in Alola. Cut trees, Strength boulders, and the like often block the way to areas with stronger Pokemon. If a trainer has enough badges, that's proof that they can handle the Pokemon who are behind that barrier, so they're allowed to use those HMs.