Gary Gygax famously relates the inception of skills into D&D as a result of having a character cross a river and someone asking "Can my character swim?" Since then skills began to creep into D&D and other RPG's at a furious pace. Eventually, most games added some skills or even made skill-based systems -- dispensing with classes altogether. Most gamers accept the premise of skills blithely, seeing them as another thing that their character can do and fail to recognize that some skills take away player agency from the table.
Player agency is the ability of the player to direct and control the outcome of the game by interacting with the narrative constructs of the game. It is at odds with character agency -- the mechanical advantage that a character has within a scenario. I'm not in favour of either extreme. That is my bias. In early role-playing games, those games with few or no skills on the character sheet, player agency ruled the day. A clever player could run a stupid character in a way that they solved all of the puzzles, negotiated with tyrants, and wooed the NPCs. The introduction of skills like perception, investigate, persuade, and deception tilted the scales in the other direction. Players could circumvent the game by picking up the dice and rolling. Neither is truly role-playing as they are either ignoring the character or the context. It is only through GM fiat in either case that pushes the players back to the middle-ground between pure gaming and pure narrativism. I abhor such heavy-handedness on the part of the GM, while others see it as part of the GM's sacred duty.
So what is a skill? In D&D these terms get broadly used to include knowledge, tactics, and actions. I think that giving a skill too broad of a definition is a problem. Survival, for instance, is predicated on the rule of three: three minutes without air, three hours of exposure, three days without water, three weeks without food. Knowing the priorities of survival is essential to the skill of surviving. These are the tactics -- the hierarchy of goals. Knowledge is knowing what plants have water, what food will make you sick, etc. The actions that you have are: pitching a tent, tying a rope, extracting the good parts of the plant, etc. If your skill broadly encompasses all of these things what is left for the player to do but roll the dice?
Let's examine Persuasion in D&D:
"Persuasion. When you attempt to influence someone or a group of people with tact, social graces, or good nature, the GM might ask you to make a Charisma (Persuasion) check. Typically, you use persuasion when acting in good faith, to foster friendships, make cordial requests, or exhibit proper etiquette. Examples of persuading others include convincing a chamberlain to let your party see the king, negotiating peace between warring tribes, or inspiring a crowd of townsfolk."
By mixing the skill definition with the tactic -- how to inspire a crowd, you have taken away part of the game. There is no need for the party to determine what the motives of the townsfolk are, to figure out what would inspire them. This was included in the skill description. Role-playing gets closed down.
Misguided role-playing theory suggests that characters are best described by a list of attributes that combine with races, professions, classes, backgrounds, and rule exceptions to yield a set of simplistic mathematical statements that determine what a character can do. If you're lucky, your role-playing game represents the modifiers directly; if not, you have a core statistic represented by a number, that yields a modifier represented by a different number, that is added to a third number to yield your total modifier for a particular action. This is convoluted madness. What we need, and have, is a role-playing game that asks and answers two questions: first, how good is your character at doing "a something" and second, how hard is it to do "the something that the player is describing." This involves both the player and the character. The rules for both of these are clear and simple, gaining greater detail with greater complexity. Because a score is reversible, a player can use 2d6 for their score of 7, while the GM has the same choice between static number and dice to determine a difficulty. This gives the GM up to four modes of resolution: both sides roll, GM only rolls, player only rolls, or no rolls involved. This allows for the player to acquire conditions to affect the odds, but the driving force behind the odds to be the character.