The problem is (imo), lots of people are accustomed to play a game just for extrinsic rewards...and that's because most AAA titles have accustomed them play that way. ie. I complete the task -> reward -> I get to see the next piece of narrative; I finish the side mission -> I get a new rare item; I beat 500 enemies -> I get a trophy to display online...etc.
BOTW is a game designed to be played for intrinsic rewards -> the act of playing itself is the reward...in the specific case of BOTW in my experience, the act of discovery was the main reward for playing the game.
Yet as I said earlier, the fragile weapons undermine the act of discovery. Experimenting with weapons on different enemies quickly breaks that weapon.
Anyway BotW is very much a reward based game, it's all about more hearts, more grip, more inventory slots, more recipes, better gear, more enchantments, while weapons were the odd one out.
Hard disagree with them undermining the act of discovery. Discovery isn't about becoming stronger, it's about finding something new. I had no issue with the new stuff breaking when I used it, that was part of the fun, you have some time with each weapon and then it's time for something different.
I also wouldn't necessarily agree BotW is a "reward-based game", but I get your point on that one. The reason weapons were the odd one out is because they needed to have some kind of reward for everything you do in the game. If weapons didn't break, getting more weapons would be pointless unless they were better than what you already have - because they break, every weapon matters, so everytime you find a weapon (all the time), that's a good reward.
You know one thing I find myself constantly doing in just about every open-world or RPG game? Stopping to sell or drop the dozens of useless items I've acquired in the past hour or two. It usually takes quite a bit, just going through the inventory and getting rid of all that junk. It's boring. And not only is it boring, it kinda nullifies the entire reward system when all the loot you get is just a bunch of crap you'll never use.
In Breath of the Wild it was rare that I ever stopped to drop items I didn't need, and even if I had to do that, I could do it in a fun way (throwing weapons at enemies) which instantly breaks them and can be useful. This is why weapons break, it makes every weapon meaningful regardless of whether they are or aren't the best.
Also, this wasn't intentional from the devs, but the weapons being the "odd one" out also made them the only balanced thing about the game. When it comes to hearts, stamina, inventory, and especially food and gear, the game allows you to take everything too far and become way too overpowered, which is the main reason why the late game is nowhere near as fun as the early game.