Anything you ignore the details of and is taken to a high enough level view will appear the same... I mean everything in the game works the same you just roll a die for uncertain elements...
Everything in modern D&D systems DOES work pretty much the same, especially in 4e! Lets face it, D&D has a special focus on fighting monsters, so yes, they add a few minor details onto the weapons ON TOP OF the 'weapon skill', which invariably applies to EVERY WEAPON IN THE GAME with some minor variation in some versions depending on if you are proficient with that specific weapon type or general class of weapons. D&D does not focus to the same extent on ANYTHING else. So your point seems very weak to me. Are you really suggesting that 4e is crippled because it doesn't have a separate skill for a Lute vs a Ukulele and there's some profound difference between them? If it was 'Rock Band the RPG' or 'Bards & Beholders' then it might matter.
It doesn't add to the character because the system you are choosing to use doesn't make using a musical instrument a character resource, instead one is forced to sub in broad vague skills with tenuous connections or just hand wave it... 5e however does make it add to the character because it is an actual resource that is paid for and can be used...
Its not a character resource because it doesn't add some kind of capability to the character. Like a weapon it is just a vehicle for accomplishing a task. Unlike weapons there are several possible tasks you can accomplish with a song/musical performance, so it could be governed by any of several skills. Honestly its YOU that wants to lump it all into one 'vague skill' where all that matters is how dexterously the character can strum the strings of his instrument and he can try to achieve any old effect equally well, and regardless of the characters insight or any other aspect of his personality at all.
Also I find it more than a little ironic that a fan of a game where it is okay for healing to take place from a totally mundane source... thinks that music has to be magical to affect someone...
That's not what I said. I said that since being able to play an instrument doesn't add any specific capability to a character that the character doesn't already have, in game mechanical terms, there's no need for it to be a controlled player resource that has to be be paid for or rationed. The player should be able to simply decide he can play or not as it suites him. If he does decide to play then NARRATIVELY, in the fiction, yes the music can affect people, it just doesn't do so to any greater degree than other options. Its possible that in some corner case being able to play might open up some otherwise closed narrative option, but given the lack of focus in D&D on playing music I don't believe its necessary to dole out playing ability carefully, any other kind of backstory can equally have an effect on the game.
But you said if it was scary music it would be Intimidate so apparently it's not diplomacy... it's DM fiat when it comes to your system. Now when talking about 5e musical talent is exactly what it says on the tin... how well you can actually play an instrument...
No, it is not 'DM fiat', if you want to scare people, use Intimidate, if you want to tell them a lie, use Bluff, if you want to get them on your side or to do something for you/that you want, use Diplomacy. I'd say if you just want to entertain them then use a basic CHA check, though Insight might also be useful as a way to determine what they'll like (other knowledge skills might work too, History, Nature, etc).
As for "how well you play an instrument" there's two answers to that. Answer one is "well enough to succeed" and answer two is "who cares?" I mean really, who cares how well you play? Narrate it as good or bad playing, its not relevant. If you want to get into a dueling banjos with Asmodeus set a DC to win and make it a DEX check if you wish, but I'd think an SC including again History, Insight, maybe Bluff, etc would be more exciting for such a unique event, and there's probably going to be a lot more involved than just the playing itself.
I don't even understand this analogy... No one does everything at 100% of their capacity, perfectly at all times... You roll dice because there is an element of uncertainty in the action you are taking... in the instant that you are rolling... either your swordplay or your musical talent is or isn't of a quality to defeat/move the opponent you face... your rolls decide that... and your narrative (unless you are purposefully choosing to be incoherent should fit said results). I mean you can blame it on outside forces if you want, but of course a better swordsman or musician could o exactly what you failed to do if he rolls high enough so it still speaks to the quality you showed in that instant. You can call it effect, though I'm not sure what "effect" is being decided besides success or failure and thus the quality of your swordplay in that moment... I don't think failing at something and narrating it as the greatest of all time is consistent... do you?
Sure, why not? Inigo Montoya fences his best and the ogre caves his skull in with an unguardable club shot right to the head. Nothing at all dictates that you 'did worse' because there was a low check. Maybe you slipped, maybe the situation was hopeless, maybe you just had bad luck. I see no reason why a player is required to narrate failure as being a poor performance. Nor is this line of reasoning useful in countering my argument, which is simply that 4e's skill system uses 'check against objective' rather than 'check against means', and I assert that the former is superior to the later and that 5e's skill system suffers for the difference.
You're assuming why music moves people... it's not always a particular message the artist sends you (and this is again why I don't like sticking it under diplomacy), as a simple example one could be moved because a particular song invokes a memory that the artist has no clue about... Or you could be impressed on a technical level because you recognize how difficult the song was... even though you don't personally feel anything when it is played... my point is music sways people for totally different reasons that can't all be placed under diplomacy... but there is no incoherence if their is a skill that represents one's musical talent at a suitably abstract level.
Sure there is, there's plenty of incoherence! I already pointed it out above. You are collapsing the whole thing down to one technical ability check that isn't even necessarily representing only technical ability, since checks represent a lot of different things. Its not better in any way shape or form.
Okay let me try to get an answer to this again... what would the background of fiddler give you a +2 in according to the 4e rules, seeing as how they are very specific this should be easy... Of course according to your own examples earlier I would need a +2 in at least 2 skills (Diplomacy & Intimidation) and possibly more depending on what feelings I would want my music to actually invoke...right?
I'm perfectly happy to give a character who has something like 'Entertainer' a +2 bonus when in a situation where knowledge of entertaining is useful, such as being on a stage entertaining people. This is exactly in accordance with the sidebar in PHB2. You might ALSO be applying a skill bonus from one of several skills depending on the goal of your music. Again, IF this game was 'Bards & Beholders' and playing instruments was a specific focus then I would imagine there would be elaborate rules for exactly which instrument works best for each task, how to play with a group, etc. Its D&D, we can live with "you have the background Entertainer and a note 'can play lute' on your sheet, so yeah, go ahead and get up on stage and try to rally the crowd in favor of the Young Duke! Diplomacy check, add a +2 for background." And, again, if the character is say a Bard and has some special magical resource that will sway people (a ritual or power) then great, that will work even better and it has its own specific rules for using that character resource, which the player paid for in some fashion or other. This is all quite clear, isn't it?