The primary thing skill challenges did was remove the design incentive to write an action complete skill system. Instead of expecting the rules to lay out a procedure for all the actions a party might take when trying to get in to a castle, they offered a framework all action declarations could be fed into. If you strip them of their narrative context, skill challenges are a terrible game; select your highest skill and try to roll well. If the GM is completely transparent, you might be able to make a calculation that a skill other than your highest skill offers more success.
I'm not sure I get what you're describing by "action complete skill system", or what aspects of D&D skill systems are lacking, irrespective of Skill Challenges. 4e has a list of skills covering adventuring (including those required to break into a castle), and lists some rules for specific uses of them, same as with the prior and succeeding editions. This sounds like you're not happy with the D&D skill system as a whole. What would you consider an action complete skill system? (I am genuinely curious.) One that lists every possible use for each skill (and no other uses are available), with equally specifically quantified outcomes for each result?
As for SC's, they're not intended to be run in a vacuum as a series of blank skill checks where a PC can roll whatever they choose. Those skill rolls function the same as any other skill roll -- there's a situation, and the player says what action they're taking, and the DM may call for a skill test, and there's a success or failure. If the action is not possible, or wouldn't help the task at hand, then the DM will likely not allow or count it, or ask for further clarification.
Given their mushy introduction, I could see cases of SC's being used situations that are not quite appropriate or what they were likely intended for. Single-point-of-success/failure tasks or even single-path tasks would not be not be a great use case. Using the example above of getting into the castle, a path could be sneak/climb over walls, another path could be bluff guards/walk in, another path could be swim moat/open locks on underwater gate/swim some more; those I wouldn't use an SC for. Something more dynamic and or extended, such as a chase, dealing with a crowd, stopping mind controlled villagers from walking into the nearby lake, perilous journeys, work much better under the SC guidelines.
I think the best and most interesting game skills (and frankly, all non-combat options) should offer is in setting a goal, and then picking from a list of available actions what will most readily achieve it, with an option to tactically reassess as the situation changes round by round.
The first part of this does sound like a typical (D&D included) skill system: PC has a goal, there's a number of ways they can achieve it so they describe what they do, which (likely) equals a skill test, which creates a result, play continues. Are you more in favor of a PbtA type game, with a limited set of specific moves that begin with "when you do X"?