So, no, the Thief-Acrobat never justified itself as a class. That parkour subgame was never particularly a strong part of a thief's game and focusing on it didn't really help. The problem with "Climb Walls" is that only a certain number of times in an adventure would it even be useful (potentially zero if the GM didn't do anything with 3D terrain), and for those limited times spells like "Spider Climb", "Jump" and "Fly" fully outclassed it.
In fact, the Thief is such a weak class in 1e that all those could have been added as new abilities of the Thief from 1st level without even adding much utility to the class.
However, yes, the ability to jump, balance on things, tumble and so forth are justified as inclusions on the skill list. And in fact 3e did exactly that, condensing down the 1e Thief-Acrobat skills into the skill system as part of its general commitment to at least conceptual backwards compatibility with 1e AD&D.