Dungeons and Dragons is a fundamentally class based game, I think that is fairly self-evident from the earliest versions of the game. Any skill-system was tacked on in the later development of the game, and whether taking the form of non-weapon proficiencies of AD&D or the skills of the Rules Cyclopedia or WOTC D&D, these skills never worked in harmony with the classes. What exactly is boundary between a class ability and a skill or a skill and a feat? I think the impetus to add skills to the game came from a misunderstanding of what a class is.
There seems to be an instinctual tendency to view the D&D classes as somehow equivalent to the Social Class of a character. This probably goes back to the original game when it stated that high level fighters could become barons. In modern times a class is most often associated with a defined 'archetype', and these 'archetypes' tend to get more and more specific so that they make the base classes irrelevant. Whether you see it as representing the social class or the archetype of a character, this view of a class necessitates the addition of a skill system.
If fighter is a PC's social class, then this means the character is a fighter and will always be a fighter unless some drastic changes happen in the fiction of the game world wherein he jumps social classes. Therefore, in order to allow this fighter to learn any skills not granted by his fighter levels there must exist a separate system to allow him to learn them. If the fighter wants to learn to Sail, he isn't going to get that ability by doing more adventuring and gaining experience and subsequent levels, he has to spend time training this new sailing ability completely unrelated to his fighter class. Thus was born the myriad of skill systems that have been invented for D&D. This essentially means a person's profession is independent of their class and that people automatically gain abilities based on the status of their birth.
On the other hand, we can directly equate a character's class to their profession. Characters gain skill through their class and they improve those skills by leveling up their class. This necessitates the ability for a character to multi-class. Training in a new class is literally training a new profession. If a fighter wanted to learn to sail they would spend time training and gaining levels in the Sailor class. Skills do not need to be separated from class, they are what make a class what it is. A person can be a Noble and also a fighter and a courtier and a spy. There is no need to explain how a fighter suddenly became a thief. These are simply professions that can be trained; If the fighter is born a Noble, that is their identity not whether they are a fighter or thief. Social status can be completely divorced from skills and profession.