Here's a piece of my theory of crafting. My apologies for any pretentiousness.
Crafting is an an unwanted/unexpected expansion of the scope of character building. What is crafting, when it comes down it? It's a form of character building. You level up, you get a skill point, you spend that point to take a skill that make your character more powerful in some way. Crafting works similarly. You get crafting ingredients, you spend them to make an item that makes you more powerful in some way. Why is one of these accepted while the other is rejected?
Maybe it's because crafting is unstructured and unfocused. The game doesn't give you a routine time and place where You Must Craft (like the level up screen for skills). It's a fuzzy system that floats around in the fringes of the game, not having a definite place.
Your theory-first approach reminds me of the discussions I read on the codex a decade ago. I will posit an alternative explanation, which should cover most of the anecdotal complaints that others have made.
Crafting is an unwanted feature because it is not gameplay.
The typical crafting interface is, at its core, a shopkeeper that performs currency conversion. Since the majority of RPGs do not generally put the players in the role of travelling merchant, the act of converting currency is not meaningful or fun.
As others have mentioned, crafting as implemented is often fixated on the gathering of materials. This gathering allows no player agency, as the zones a player can access are gated by non-crafting activities. Even the collecting of materials is not gameplay because the player must wait either for a random drop or for the designers to decide the composition of the next area allows for gathering something useful. Solving these problems with gathering is unlikely to make
crafting engaging because that's not what crafting is. A blacksmith doesn't waste his days digging coal. A chef delegates shopping in the market.
For crafting to be truly compelling, there must be gameplay attached to the act of combining ingredients into new items. The simplistic approach here might be some form of mini-game. A proper approach would be create an entire game about crafting, not gathering, and distill those elements into a new template for crafting systems. A crafting game would want to incorporate elements of technique, mastery, efficiency, expediency, and creative use of basic techniques for advanced outcomes.
That's my theory. What would a game that accepts this theory look like if it asserted that crafting was a desirable feature?
A corollary of this theory is that crafting cannot be designed as it is today, as an add-on system by a junior designer who is instructed to create a time-sink. Crafting progress must have effects that players can see and look forward to improving.
This example is purposefully simple to illustrate the concept of "crafting as gameplay". I will use elements of Diablo II and Spacechem because people should be familiar with those games.
-Consider that weapons can have the properties they have in Diablo II: damage range, critical chance, speed, elemental bonuses, chance to cast a spell, a passive boost to skills, etc.
-Consider that crafting involves taking various enhancement components purchased or acquired through other game systems, many of which are tied to the listed weapon properties. (blue gem = slow on hit, rare rune = chance to cast nova on hit, etc.)
-Imagine that crafting to improve your weapon is not about combining materials, but
how you combine materials. Instead of socketing an item, you go to a workbench and tinker with the item in the same manner as editing a factory in Spacechem. Different weapons have different properties based on their craftsmanship, and type. For example, more space to tinker with or additional waldos to manipulate.
-Crafting unlocks would include the additional assembly line instructions that become available as you progress in Spacechem. By creating these new crafting 'techniques' in various ways, better results can be obtained.
-Crafting choices determine weapon modifications. For example, the faster your crafting can take inputs and process them into outputs, the greater the weapon's haste. If the design also incorporates a red gem, which will hamper speed, the result will have fire damage. Is this a worthwhile trade-off? Well that depends on the monsters you are facing, and other character build choices.
-More potent crafting unlocks can come in multiple forms. Some can be strictly better, a numerical upgrade or a component that provides the same benefit while taking up less space. Others could be more drastic, such as reducing the crafting area to provide a passive +3 to a specific skill.
I've described an approach to offer item enchantment as "crafting gameplay". A similar design may also apply to an alchemist's lab. Leather working would be less applicable.
