That is a whooole another story.
It's different, yes, but parallels still exist. You can't just do what you do in P&Ps in cRPGs, but some of the same reasons you're offering a wider array of skills in a P&P still apply, and it being party-based is one of them.
Imagine we're using New Vegas' SPECIAL, with its heavily stomped down and narrowed down skills. How do you even make 4 useful characters in that system with quickly replicating skills and making them interchangeable. A very broad skill system right off the bat helps define your different play characters, and because you have four times as many skill points to check the singular value of investing skill points at level-ups is less of a concern. That's true for any party as a whole, whether it is a cRPG or a P&P game. In a party, I can spare some points to specialize a doctor or an outdoorsman without having to worry about crippling myself for a game, but instead knowing I should have some specialization and niche skills because a wide set of skills will see usage of the game and narrowing it down or taking the same skills over and over just narrows down my gameplay experience.
That's how I see it, anyway.