I never really minded it a whole lot but didn't particularly like it either. On one hand it's theoretically kind of an interesting way of resource management by giving you the option of throwing weapons to get more damage out of them (which might actually be invalidated if the last hit before the weapon breaks is always critical anyways, which I'm actually not sure of since I don't care to research now) and on the other hand there's the edge case of ending up without weapons, which I don't think actually happened to me after a certain point. If anything what annoyed me more often was that I'd run out of equipment slots which would either: a, make the time I spent trying to get extra chests in shrines useless more times than I can count, or b, mean I'd have to spend more time choosing what to drop so I could take the new weapon.
The most interesting thing I can think of that comes as a result of weapon breaking is how it could, in theory, put you in situations where you'd have to find ways to take enemy weapons, which unfortunately almost never happened to me either because of how many weapons I'd have at all times. Even the few times I decided to raid camps I'd just leave most weapons lying around since I had better ones anyway. Eventide Island is probably the notable exception here, where the survival part is actually there.
I remember thinking before release that the weapon breaking might make the game more survival-focused. The actual game feels more like one of those that throws loot at you constantly in order for you derive satisfaction from seeing your numbers rise and rise. I imagine at least in those you don't have to throw weapons every time you get a new one though.