At this stage in my playthrough, I often have to explicitly toss out weapons because I have too many -- very rarely do I run out of weapons and have to farm.
I actually disagree with it being well designed. The weapons are too common and break so frequently I feel like I'm playing a weapon changing simulator. They have never been a limitation and I have never worried about finding a new weapon to use. However I do find myself constantly having to bring up the menu to change weapons. I have 12 weapon slots and pretty much every slot is a knight's claymore or guardian weapon.
Once you get to the point of farming the world minibosses you'll never find yourself wanting of a good weapon. Hinox and Lynel have good weapon drops and they drop pretty frequently.
I feel as though weapons should have been made more rare but more durable so that there were times when you wouldn't have a weapon because they were rare to come across and you'd second guess yourself about using your weapons on lesser mobs like red moblins or keese.
I find myself needing shields more often than weapons - since I like to go Guardian hunting and I kill them exclusively with shield parries. One or two missed parries and my shield is destroyed. While I rarely miss the parry anymore, it does still happen.
In other games you can end up with ridiculously overpowered gear, and then cheese your way through all the areas of the game that are note late game.
If you do this here, you will waste very good weapons on enemies that are not very hard. Then you'll pick up their middle-tier weapons. Or you'll just preserve your good weapons by not wasting them on cheap enemies, which actually makes things more fun.
It also runs the other way. If you go straight for Hyrule Castle you'll actually find precisely the kind of weapons you need for Hyrule Castle there.
You can sneak into Hyrule Castle in the early game to get great weapons, but they won't last forever.
The power issue is separate and can be resolved (or not, it's sometimes fun to immediately feel like a badass while never being invincible) in a lot of ways. I don't really see how permanent weapon damage would make much difference in those tradeoffs, at least compared to a game that has repair.
It's a little sad to see that awesome sword you kinda got attached to break, but....there's always something new to try. Two-handed spears, giant hammers - adds nice variety.
I'm yet to farm anything.
But now I have 4 or 5 more weapon slots than I started with and 3 additional ones elsewhere. And they are all full of different weapons. Now the hard part is figuring out which ones to keep when I come across new weapons, so I'm usually happy when something breaks because it takes the decision away :p
Weapons are dropped off of almost every enemy, and were never a problem to get, though there is a fairly high churn rate- most weapons have like 50 strikes in them (maybe 5 battles) before they break. There are a number of weapons with significantly more than that though (Zora's Diamond spear is like 300 iirc)
I never had to farm anything in that game though.