To me, the idea that each character would have a different approach to builds is a little odd but I can easily imagine how it would work.Does player B make an ability check to swing across, player F make an Athletics check, and player T make a Rope Use check?
What if they're not trained in any of these, is it worse than a simple ability check? Do they all use the same DC? Is player B going to be hosed because he's using a less complicated system and doesn't get a "+3 for trained" bonus? Is player T hosed cuz he chose "Rope Use" but didn't invest enough points in "Swing" skill also?
1. Even in 3e, each skill is a group of "related activities" that you're trained at doing.
2. Each choice (ability checks, 3e skills, 4e skills, &c) is a different way of defining "what counts as related activities".
3. Monte's team has the task of balancing different methods.
Therefore, in the example, perhaps for the OD&D character he could be good at all Dex skills whether they use a rope or not. The 3e character is equally good because he has rope use trained and this would apply regardless of if the rope application seemed to be based on Str, Dex, or no ability at all (aka tie a knot). The 4e character is also equally good because he is trained in Acrobatics (aka swinging on a rope versus Athletics which is climbing on a rope) but in this case happens to be a Wizard and is bad at all other physical activities (the player took Acrobatics based on some wonky background concept

It is possible to make this system work, though tricky. One player "groups" the situations they can handle by the prism of Str-Cha. Another player "groups" the situations they can handle by the prism of niche specializations. A third player "groups" the situations they can handle by the prism of skills that are a blend of attribute flavor and training flavor (aka 4e).
Balance comes in making sure that each character is "skilled" in an equal number of circumstances that the party encounters as long as they're all playing the same class. I.e. a party of 100% rogues where each rogue would shine in skill checks an equal number of times across the life of the character no matter how they each "grouped" challenges, aka skills. Once you throw multiple classes into the mix it will be hard to discern balance if 5e uses the 3e conceit that skill points per level was part of the balancing mechanism between different classes (without actually using points in all systems).