Seems to me that this can be fixed with a single line somewhere in the relevant classes (or subclasses) about using Dex instead of Str.
On the other hand, a "Wallcrawler" feat would seem a welcome addition, IMO.
I think a bigger question is whether it needs to be "fixed" at all, since that seems to be of some dispute. I agree that Hollywood has a tendency to make climbing seem much easier that it is in reality, although climbing is far from alone in this regard. (I am personally constantly amazed at how jumping into the ocean or a lake or any body of water in darkness generates a mysterious ambient blue lightsource around the hero. 13th warrior has a brilliant example of a long swim through cave that features no bumbling in aquatic darkness.) I think this is one of those areas where one player's heroic fantasy gets in the way of another player's suspension of disbelief (or vice versa).
Generally, I think it'd be smart for D&D (almost any rpg really) to work such conflicts in such a way that both decisions are possible on a "by table" basis. That's a tough thing with D&D, though, since things ..well naked Barbarians, Warlord Healing, heck HP. ::shrug::