This is actually something I have put a lot of thought into as I have tried to focus my programming skills into the creation of a CRPG and I find the classic RPG tropes to be inadequate. I dislike classes because they force the player to make a huge decision about the gameplay mechanics before they start playing the game. The classless systems work better at the beginning of the game but quickly start forcing the player to grind their way to god mode. The Elder Scrolls are a perfect example, you get to the point where you can't advance you character unless you start using skill outside of you "class". The level scaling only exasperates this problem. I felt there had to be a better way, skip to the bottom if you don't want to sit through my crazy rambling.
Instead I have opted for an Attribute based system. There are several attributes but they fall under the 3 classic categories; they are Physical, Social and Magical.
Physical Attributes describe the physicality of the character, they are things like Might and Endurance. Physical Attributes govern skills used in combat. Social Attributes, such as Charisma and Perception, describe how the characters manipulates the world around them and covers skills like Speech and Stealth. That leaves Magical Attribute to cover all the Magic Skills oddly enough.
At character creation the player distributes points amongst the attributes, just like every other RPG ever made, and this determines their "class". Skills are raised by using them, but how quickly they raise and how high they can go is entirely dependent on the number of attribute points in the governing attribute category. This way a "wizard" who ignored Physicality and put all points into Intelligence and Wisdom will still be able to pick up a sword, and can even increase their skill with it but not very quickly and not by very much. If you want your wizard to be less "squishy" you can transfer some of those points to the Physical Attributes but then your magical abilities will never become as powerful as they could have been.
Each of the attribute categories also has a Null Attribute. Instead of investing in Magical Attributes you could use some, lets say 5, points to purchase the Anti-Magic Attribute. You are now have zero magical capabilities/weaknesses. You are a skeptic, you don't believe in magic and cannot use it at all, but it also has no effect on you because it's all a bunch of superstition. Magical fireball don't hurt you but magical spells can't heal you either. Weak healing potions are ineffective "snake oil" and the most powerful of healing potions are no better than basic medicines though they do help, a little. Anti-Physical characters are just spirits in a material world. They cannot wield weapons or armor but cannot be harmed by them either. Anyone choosing to be Anti-Social will never engage in dialog and never barter, they are so hideous and smelly that no one can go with out noticing them. This is your crazy old hermit type who finds what they need and throws away what they don't.
There are also antagonistic skills which allow you to only use one at a time. Say a wizard wants to specialize in Necromancy, they get to the point where they can kill everything in a room by filling it with poison and then resurrecting all the victims into an army of undead minions, but if they are hurt personally they are inept at casting a simple healing spell on themselves. If they want to get better at Restoration magic then they can keep using it and level it up to the point where they can completely revive a fallen ally, but they must sacrifice all their Necromancy powers to do it. Warrior types will have an easier time going from wielding a dagger to a sword than from dagger to war hammer. This allows a player to essentially respec their character if they don't like the choices they originally made, but not in a manner that allows them to tailor the character for each specific quest right after it is given.
TL;DR
I feel that a system like this would offer full flexibility in skills and equipment to the new player. It is not until the player advances they start getting less choices of how they play so that they grow into a strict limiting class only in the later game.