Honest question, and I'm not trying to be combative here: Do any of the major competitive games with (at least somewhat) deep mechanics explicitly teach users when and why to use different components?
I feel like most of them just state what they are and how to do them, but not why or when.
Does LoL teach the intricacies of the different characters, abilities, and items? Does DOTA2?
It has mouse over tool tips that explain what an item or skill does (like it might say Sword of something - +1 attack restores hp over time). Some of them say what kind of character it is, support, carry, tank etc which then gives you an idea of the role of said character. Like, even if you don't understand games I think you'd work out a "support" type character would be one to offer support to the team in a team based game.
Does CoD teach users what good combinations of guns and abilities they should look into? When is appropriate to use streak bonuses?
No, but it does say what attachments do (and shows how it affects stuff like weapon damage, range etc) and it tells you what the abilities and kill streaks do and how much points you need to use them in a match.
I don't think Battlefield teaches players about squad communication or even what the standard progression of most of the modes even are.
I don't think so but the keybinds pretty much tell you that Q (or whatever) is to mark/call out and hold is for the communication menu which while not something like proper voice communication and strategy is a mechanic in the game. And I think the menu tells (or did when it was a menu) what to do for the modes (like capture points, blow up gold etc). I think it said that on the loading map screens? I don't know since they went to battle log and having all the menu stuff outside of the game.
Dark Souls doesn't teach shit all about weapon properties or any maneuvres (spell cancelling, attack cancel dodges, etc).
Well it does tell you weapon damage and type, the stats needed, the type of weapon (great sword etc) but no, it doesn't say about things like animation cancelling but I don't think that stuff is intended. Like, you can mash on roll and find out you can dodge out of an animation before it should end or something it's not like an actual intended strat.
Do RTS games teach users about good build orders?
Not to my knowledge but the SCII might, not played it though.
I honestly think a lot of deeper games are designed around the ethos that player discovery is part of the game. They will teach you how to do something, but not what specifically it does, how it's used in the meta, why or when you should use it, or what else it affects.
The thing it, even in games where it doesn't tell you why or when you'd use certain things it gives you enough information to work it out yourself. Like in CoD it tells you what a silencer does, makes your gunshots not show up on the minimap, with that information you can then implement it into your strategy. SFV doesn't tell me what Karin's V-Trigger does so I can't implement that into my Karin matches (or know what to do against it).