Most people who say A16 / LBD was great follow it up with the caveat that it did need work - ain't nobody liked hugging cacti for "armor use skills".
You're just conflating the terms there - LBD is "use a skill to improve that skill"; general XP is different. It's not LBD to become better at cooking by bashing zeds.
So perhaps I exaggerated. This conversation tends to lead a bit to that. No, no one said it was perfect. But they do point to it as being what they want. My point was about what I responded to -- they obviously did try it, unlike what was stated.
There are a variety of ways games do LBD. Skyrim style (or Morrowind, if you want to extreme version) is not the only way. People who like that method tend to treat it as the only "real" LBD and that nothing else is LBD. However, it really is no different to improve your ability to use a weapon to kill by swinging it in the air at nothing versus killing things to get experience that you spend to improve a weapon skill/perk. Yes, general experience lets you choose what you improve without having to spend time doing a specific thing 1000 times, but in the end, you are still improving your abilities by doing things. If the game separates my kill experience from my mining experience from my crafting experience and I use each individually to improve those skills, or if the game has all of that combined into a single experience pool and I use that to improve my skills, I'm doing the same thing.
The difference is player choice. Instead of having to jump thousands of times to reach parkour 4, I can instead just do a lot of killing of zombies. Instead of making it about gaming the system by jumping everywhere, I instead play the game and kill zombies, which is what the game is about. Instead of "hugging cacti" to improve armor skills because it's more efficient than fighting zombies, which you might do without taking damage, I can improve those skills by actually fighting.
For people who want to mainly mine or craft or farm or cook, they can do so and still improve their fighting skills so they can go out and fight decently whenever they want to, without having to spend hours swinging a weapon in the air or jumping around or sprinting everywhere or hurting themselves repeatedly or whatever else. They can do what they want in the game and still gain in abilities that are unrelated so if and when they want to do something else for a bit, they can do so without being underskilled.
You have a group of players who prefer the Skyrim method. These tend to be players who have a lot of time on their hands. They enjoy having to do a lot of random stuff to improve in their skills, regardless how much wasted time it takes where they aren't really playing the game. Sure, they can gain skill experience by playing the game (killing stuff, or whatever), but if they want to be efficient, it's far faster to gain most skill experience by doing random things that aren't really playing the game. But they like that.
Then you have most other players who don't enjoy spending time doing these random things to get better, but prefer just to play the game. They tend to have less time on their hands (I'm not referring to casual gamers, just to be clear). They enjoy going out and just enjoying the game itself, whether that's fighting, crafting, mining, building, etc. They don't want to have the efficient way of improving be something like jumping everywhere they go or swinging their weapon constantly while they are walking around.
Neither option is right or wrong. Neither option is better or worse. Just because some people like one over the other doesn't make it factually better. It is nothing more than personal preference or opinion. In the end, you will usually find that most players don't prefer the Skyrim style in games. To be clear, if a game uses the Skyrim style, the people who tend to choose to play the game will usually prefer that style, so it appears that the majority of players prefer that style. But that just means those games lose out on a lot of potential players because those players don't like that style. I don't have any general poll results that aren't tied to a specific game that shows how many prefer Skyrim style versus non-Skyrim style, but I have a strong feeling (I admit I could be wrong), that more than half of all players (still not counting casual gamers) prefer a general experience pool over Skyrim style for improving skills. That doesn't mean they won't play a Skyrim style game, just like those who prefer Skyrim style will still play games with a general experience pool. But if you're looking solely at what people prefer, I think most prefer a game that gives players the choice of how to level up, regardless how they gain the experience.