You could always just charge off into the distance too. Running away from pretty much everything characterised my earliest exploration efforts when I took off searching for towers as soon as my rented paraglider touched down after I escaped the game's tutorial area. I dashed off trying to discover all of the towers to uncover the entire map, except that I couldn't fight or survive against the enemies, so I had to work out 100 different ways to cheese it and charge off into the middle distance.
The thing is, this made me feel smart in a way that unloading a shotgun into waves of demons doesn't quite manage, and the game doesn't stop there. The Legend of Zelda: Breath of the Wild is a series of puzzles, puzzles built upon puzzles. Climbing stuff requires thought, completing the game's side-quests requires planning and knowledge - or, perhaps, finding a random salesperson that sells the item you're trying to collect - but even then you'll feel smart for finding a way that saves you having to do any busywork.
The greatest example is the fact that, as soon as you finish the tutorial, there's no stopping you from charging off to the castle and trying to take on the final boss, Calamity Ganon. There's no chance of winning a stand-up fight with Calamity Ganon or his castle minions in your low-level gear, but with some smarts, you can give it a shot even if you will probably fail.
Breath of the Wild is a game that trusts you to explore and learn by yourself without holding your hand. As a result, there's an extra kick you get when you do something stupid that pays off: Realising that the metal weapons Link carries are just as conductive as the metal objects the game gives you to solve electricity puzzles with was a revelation, for example, and resulted in me "cheating" my way through them with only a handful of metal items.
Take the desert town of Garudo. Getting across the desert is tricky, and your horse is having none of it. To get there, you could choose to run across the desert, but you'll cook in the hot sun. How do you get around that? Well, you could cook and eat food that keeps you cool, or you could try to make your way across the flats in the shade generated by rocks where it's cooler. Perhaps you'll choose to travel at night when the desert temperatures are low. Or you could strip, and run there in your pants.
Breath of the Wild doesn't make any of these options clear to you. It doesn't care. It trusts you as the player to work things out for yourself.
I've never encountered this thinking in a game before where every different aspect of the game can be solved in a variety of ways with all of them feeling valid. I think this is why The Legend of Zelda: Breath of the Wild works so well but also why it makes every other open world game I've played recently feel shallow and disinteresting by comparison.