And yet, doesn't this also fit the social aspect of the game? Instead of having some social-conflict-resolution mechanic or skills like bluff, diplomacy or intimidate, why not just have it part of player backstory (Ariadne grew up a noble's daughter, and has a good command of etiquette and intrigue), and just dispense with skills or mechanics?
Wouldn't this also apply to combat? 'Ariadne also trained in fencing, at her uncle's salon, and got to be better than most of the spoiled young men who fancied themselves 'better than any girl.'' When combat shows up, the player just describes what she does, and, if the DM feels it is utterly necessary, he can make some dexterity check or something to see if she manages the graceful disarm she mentioned, or a strength check to see if she really snapped that dude's sword in half.
It all comes down to what is important in your games.
It does. And what is important in the core D&D game is killing monsters, RPing with monsters, NPCs, patrons and the like, and taking stuff. It is fine, great even, if that's not the way you run your games, but it IS the core assumption, the way most people play the game and the playstyle the game is designed for. Asking why social and combat skills and powers are in the game is a bit silly and doesn't make any kind of point. The encounter, and its resolution is the cornerstone of the D&D game. The 4e game system includes rules to resolve those conflicts, even those conflicts that involve something outside of the more normal adventuring means - such as crafting or performing. The rules consist of advice on winging it and a few tables on DC by level, skill challenges and the like.
Choosing a game system, then playing that game in a manner well outside of its core assumptions (the game is about adventurerers adventuring), puts you in GM creativity territory. Twisting D&D into Lutes and Lyres is certainly possible, but complaining that the rules for doing so were left out is a bit puzzling. If you use the D&D ruleset to play a game that isn't about adventurers, has no monsters or loot, and no combat, more power to you. But there are better systems.
Crafting is superflous. Some DMs/groups like to use it, most don't get much out of it. I'd much rather have a streamlined, balanced ruleset from which to work, rather a bloated ruleset full of subsystems and gaping holes where these subsystems react with each other or the basic rules. Trimming the game back from rules bloat is much more difficult than creating the rules you need for your style or shopping online for 3rd party supplements that fit your playstyle.
Gamers are a creative lot and its quite easy to modify a game system to fit your needs. And when you modify the game for your own group, you don't have to worry about what kind of brokenness that is going to open up in the land of munchkin. If you design a craft system for your group who loves craft systems and it has holes the size of krakens, it won't matter much because your group will play with the spirit of the rules. If those same rules are part of the core system mechanics, then its a problem for the whole community. If your players look for ways to abuse your own house rules, beat them with sticks until they learn better.
Gamers are also armed with a robust and creative online community that designs, often for free, entire system modifications, subsystems for practically everything imaginable, forms, aids, etc., often just for the joy of sharing their creations with others. If a complex and robust set of crafting mechanics really has a niche in D&D gameplay, the 3rd party publishers will tackle it, put out some great rulesets and there will be no need for complaint that the designers did not cater to your particular niche of needs for your particular gamestyle.
Combat and encounters are assumed to be part of ALL D&D games. And in the default game, it is of little matter whether your sword was bought, found, stolen, crafted by you, an heirloom... those are background details and belong as such.