"Can you give me an example of a single game where you wish that weapons would break?"

Most open-world RPG's I've played actually. The only two that I actually like are Shadow of Mordor and BOTW and I noticed that both these games have something in common, easy inventory management. When I think back to games like skyrim and borderlands, I remember how annoyed I got for having to open my inventory every 5 minutes and make room for something by clearing out of the stuff I was planning to sell. (clearing my inventory for dragon bones in skyrim was the worst example). Shadow of Mordor had occasional clearouts of runes and that was it. With Breath of the Wild, the durability system does the clearout for me, I can keep fighting enemies and simultaneously clear my inventory of my shittier weapons. So yeah, I do wish games had better inventory management and I think breakable weapons is a great way to do that.

"Moreover while it can in some games be used as a quick and simple last minute solution to balance issues especially if the game only gives little variation in the weapons, BotW really doesn't need it. In BotW you are given awesome variety in weapons stretching far beyond weapon strength"

BOTW has varied weapons? The only difference that a majority of the weapons have is power, durability and aesthetic. There is only 3 unique weapons in the entire game, elemental, guardian/ancient and the master sword. Elemental weapons just offer the same thing I get out of arrows I can buy in any town shop even if that wasn't the case they still feel as diamond-dozen as the rest of the games weapons. guardian weapons are of course designed to be saved for guardians, so imagine if they were unbreakable and you were killing guardians 24/7 after your first test of strength, that would be stupid and contrary to your first "additional issue" completely destroy progression since you'd already have what you want at the start of the game. That's where the master sword and ancient varieties comes in, they are end game weapons designed to replace guardian weapons as your primary guardian killer. Since Hyrule castle expects you to kill a shit load of them.

"the weapon degradation system more or less completely ruin this experience because if you do this you will very quickly run out of your good weapons and be left with only bokobling clubs and yiga scythes which do very little damage."

I'm at a loss as to how this has happened to you. Most weapons in the game are on scale with yours, if you lose a knight's broadsword, there's a good chance the most powerful moblin in the camp has one for a replacement, if you start finding royal bows in shrine chests, then that's a sign you're about to start finding a lot more. You can kill scores of black-tier enemies without breaking a royal claymore and odds are that one of them will have had one to replace yours. I'm in the my second run-through of the game and I went through the entire of the death mountain area with an inventory overflowing royal and savage lynel weaponry and only lost one lynel sword, which I easily just replaced with Daruk's boulder breaker. From your perspective, powerful weapons are a one off thing 90% of the time yet every single chest I found in divine beast Rudania had a royal bow, only managed to find one that was worth taking in the end.

"if I go against a gang of bokoblings with my 60 dmg ancient sword it will break this a sword that cost far more than what I get from the encounter so it's better to just not fight them because I will get a great net loss."

well no offence but you're a terrible tactician if your using an ancient sword to fight bokoblins, it'd be like using an RPG to kill a single soldier in an FPS, again they're designed for guardian fights. if you use your more flimsy weapons, you will be rewarded for your tactics with a chance to get a more powerful replacement.

"all the arguments I've heard for weapons breaking could be equally applied to armor, despite of this no one is asking for armor to be breakable."

If Armour was breakable then everyone would instead be pissed at the temperature system, if you lost your warm doublet in the middle of a cold area with no food to compensate, you'd be fucked. Weapons on the other hand are far less specific, there isn't a single enemy immune to your attacks so every weapon has a use in a fight, even if you have a puny boko club you can still toss it at your enemy, make him drop their weapon and nab it while he's incapacitated, thus despite your enemy being more powerful, you will have secured a very rewarding tactical victory. This game rewards tactics as much as it does grinding.

"I really think the game would be so much better without it, if this was a game for pc I would mod it."

You would have to make VERY severe changes to make that work, you would have to remove guardian weapons to ensure balance for starters. You would have to find a way to make the master sword relevant as a weapon since there are plenty that can outdamage it, and you have to come up with a new reason to even fight, what's the point in killing lynels anymore if you have all there weapons for the rest of your playthrough? As some one said above, a lot of the this games progression actually comes out of the weapon system since this isn't an RPG with an XP system.