OMG what are you talking about ? This a CLASSLESS system...
Of course it is, but you still start (and can level up) skills that require ITEMS and are used in specific ways and this is nowhere said in the game, like that you can use Anvils to repair items if you have a certain skill, how many players you think know that?. Both systems exist in old games, so you can't chalk this of to player experience. Game needs to say what item is needed for a skill, what is craftable in the inventory and what is a quest item.
The game needs to actually say that you gain new abilities by buying them, this isn't at all transparent to a new player. As stores aren't marked, new players may get confused where to buy anything related to THEIR class/playstyle to boot. In this case the game also needs to improve the markings around towns, I mean that in the virtual sense, there needs to be notation of "Vendors" on the maps.
What you write as obvious is not what I mean at all

Crafting is exactly NOT obvious because nowhere in the beginning of the game are you ever asked to craft anything. I would bet with you that the majority that is interested in D:OS has no clue about crafting and will never have a clue about crafting, unless they read this forum or watch a let's play where the player has that clue. Dragging random items over other items in your inventory is absolutely NOT intuitive (anymore). Don't forget that games have established different methods for crafting for many years now. And the biggest games (Diablo 3, Skyrim) have dedicated systems for crafting. We can't just act like that's not a fact.
That aside, I think I get what you are saying and agree, the skills are really bland and thin in their complexity so the tutorial in the normal sense may not be required, but they are still opaque to new players all the same.
The worst thing Larian can do imo, is not take the problem of the "missing beginning" seriously. Of course I don't want a run-of-the-mill pop-up string tutorial in an unskippable boring sewer (Oblivion!). But there must be some better way to begin the game than just plopping us on the road with no idea what to do or where to go.
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Heck it needs to be only a simple INN where both our chars wake up after a binge drinking night, finding their stuff gone and the door locked. This short sequence could teach players all there is to know about the game-systems, and via character dialog tell us what we are doing and why in the process. And maybe interlink that with the story of the murder in the town. Give us some motivation, some background, some tutorial. Not insanely much, just enough to get us going.
or in fact, your Academy idea, with good written quests that teaches all that. The setting doesn't really matter, it's just a matter of teaching players how the game wants to be played. As opposed to teaching players how parts of the game are played.
As long as it's all optional. ^^