And that's why 3e isn't a game that brings class-based and skill-based together in the way you seem to be claiming. It hinges upon classes, to the extent where skill-based customization becomes impossible without bringing in classes (like clerics and healing or rogues and trapfinding).
Yes, point-based games can lead to shafted characters or characters that make little sense, but that is entirely the point of point-based over class-based: you can make anything from the disparate components at your disposal, as opposed to taking a pre-built package (class) which defines your strengths and limitations. Any attempts 3e made towards this model were half-hearted at best, as picking up new class skills, aka "skills I don't totally suck at", required you to multiclass, something you could only do to a particular extent. And that doesn't even touch on the fact that some things are only possible if you pick up another class (like trapfinding, an ability limited to ONE class).