I went into BotW expecting a standard Zelda and spent the next five hours disliking the experience and trying to force myself to like it. At a certain point I abandoned my idea of "mainlining" the game and started exploring and climbing mountains just to see what was in the world and where I could go. That is when I fell in love. The game is a beautiful and relaxing experience that encourages and welcomes players to experiment with the systems, explore the world, and partake in a true adventure game unlike any made before it.
Miyamoto says that the original Zelda was inspired by his childhood adventures through the hills and mountains of Japan. I think Breath of the Wild is the first Zelda game to completely fulfill that vision. It's a game that's fundamentally more about the journey than it is about the destination.
The lack of standard Zelda dungeons is lamentable, but I don't think that takes away from the game's quality. Rather than a simple lock-and-key system that most Zelda dungeons operate under, the dungeons are a way to interact with and creatively explore the games systems of fire, electricity, wind, and ice.
I could go on, but I think BotW is a unique experience that everyone should try, though it might not stick with those who prefer more structured games.
Addendum: I think the weapon durability system is a positive for the game and encouraged me to think creatively on my feet when fighting enemies.