Rain does a lot more than just create slippery cliffs though; it drowns out the sound of your footsteps and reduces enemy vision, making stealth more potent. It buffs electrical weapons, as hitting a wet enemy with one will not only do more damage but also create a lightning AOE. On the flipside, bomb arrows are extinguished, not just for you but also for enemies. It creates puddles, which offer up opportunities for both electrocution and using Cryonis. Different animals come out during the rain.
All of this is indeed really cool, but ultimately, not being able to climb is just a bigger nuisance. It's one of those things that didn't bother me as much in most of my first playthrough because, as annoying as it was, I knew that at some point there would be some gear or power-up that would allow me to climb in rain more effectively... but no. If it's raining, it's raining and you just gotta say "oh well".
The real problem with elements like that is, while interesting at first, in the eyes of some, they eventually become an annoyance that gets in the way of what they are trying to accomplish. That's part of what makes mods so valuable to the long term viability of a game. It's also why game developers need to get over this "play the game the way we intended" bullshit and learn to provide options. People like and dislike a vast array of features and settings. What one person loves, another might hate. Allowing people to tailor their experience is a consumer friendly solution.
Consumer friendly, maybe. Art? No. As a purist myself, I'm very much not a fan of this idea that more options is always a better thing.