I don't really understand your criticisms, especially those that focus on aspects of the game that are ancillary towards it feeling natural. Horses are wildlife. Rain is a natural weather occurrence. Fishing rods are stupid. All of those elements are meant to enhance a certain atmosphere (the same can be said with the music, which I constantly hear dislike towards, and I constantly don't understand), which I think the game nails. It's about going on an adventure. It's about gaining courage. If you feel that your experience delivered that, I'd say the Zelda team did a pretty good job.
I don't really feel that the Divine Beasts could be considered a negative element either, except that there's a clear sense of growing complexity in how you should tackle them, rather than all four being equally difficult. I'm also surprised you fault the four main bosses, but not the final boss. Anyway, of course there's room for improvement. That isn't to say the game isn't one of the best products on the market right now, or even that it's not great. I really don't get this argument, because people bring up Ocarina of Time as one of the best Zelda games so often, even though there's tons of room for improvement there, that later games then delivered.
Glad you liked it though.
Let me clarify my statement regarding horses since I did not provide much detail, I feel they are too restricting to use and because of that I barely road mine. I do agree though that them being apart of the wildlife is a great feature, that isn't my complaint, it is that they were more hassle then they were worth to me when it came to horseback riding especially them needing to be in the vicinity in order to call them. I understand why they made that choice for realism I just hope in future games they find a better way around it.
In regards to rain, I don't mind the weather system but I feel the rain can halt exploration way too often and it happens too much for my taste. If they had a way to negate slipping while climbing, whether it was an armor set or some other ability, that would have been fine, they had a way to limit lightning strikes.
Music, I state I felt it was decent, just not memorable like previous Zelda's. Like many of my "cons" they aren't really what I would call horrible, just things I hope they work on for future games.
Dungeon bosses, I felt they were uninspired in character design and I didn't find them that engaging when facing them, I actually enjoyed fighting Ganon and how he looked. I think the only dungeon boss I found interesting was the desert one. Overall I had far more fun facing the boss esque creatures in the overworld. In fact some of my best memories from this game will have come from them. The dungeon's themselves aren't bad, but I found the shrines to be more interesting. They have one feature that I would like to see further explored in future games though (Sorry I'm attempting to be vague to not spoil things). Honestly I think it is a testament to the game itself that I didn't feel it needed the dungeon aspect of the divine beasts. I have a feeling years down the line I will barely remember the divine beast dungeons or the boss fights.
Fishing rods, they may be stupid to you, but I enjoy the serene and calm nature of fishing in games, whether it is Zelda, Animal Crossing or something else. Bombing or swimming up to fish in order to catch them doesn't offer the same amount of joy to me. It seemed to be an odd feature to leave out, especially since the game is built around exploration, I think it would be wonderful to find a secluded pond or lake on the map and fish perhaps even tie it into some quest.
Overall I think my biggest complaint about the game are more the performance issues (slow down has always been something that bothered me). Everything else in the cons are more personal preference and things, while decently implemented, could be improved. It doesn't change the fact the game is one of the best games I've played in years and nails open world exploration in a way that few games have ever done.
Also I don't believe I said anything about other Zelda games not having room for improvement. Twilight Princess is my favorite out of the 3D Zelda's prior to Breath of the Wild, and even that has room for improvement. I adored Wind Waker but realize it had issues as well. With Ocarina of Time, I think that game gets a pass because it was pretty revolutionary when it first came out and helped inspire various mechanics in gaming, it is similar to Super Mario 64, while not perfect had such an impact that its faults are easily overlooked by many.
I've yet to play a game, period, that was perfect but that doesn't mean they can't be great and BOTW is one of them. Even after finishing it I still have a drive to play it, which is odd because I tend to be someone that isn't a completionist in games and when I finish the main game I move on to something else. Time will tell where it ranks compared to not only the Zelda series but my favorite games period but it will be well up there.