4E wrote mechanics for things that many DMs had been doing for a long time - requiring PCs to make rolls to do things where there was a chance of failure. All Skill Challenges did was group them together and provide a group mechanic.
I felt like the sin of 4E Skill Challenges were encouraging overcomplication of simple situations. I saw skill challenges being used where the structure of the challenge was more important than the story being told. The DMs set up a skill challenge, a player/PC came up with a solution that negated the concern, and the DM did mental gymnastics to stop that very clear solution from solving the entire challenge, because he'd planned for 7 successes before 3 failure.
Your approach is in the direction I went, but I take it farther and just say: There is no such thing as a skill check. There is just a situation that might be addressed by ability checks, spells, or other things. I give them the situation and see how they approach it. That might take several skill checks, where some failing may be disastrous, and others might just cause a setback, they might bewitch someone and end it, they might just fly past the challenge.
I think looking at Skill Challenges is a great thing for breaking down how encounters may be constructed, but once you understand it, being bound by the rigidity, even when simplified, of a Skill Challenge detracts from immersion.
That being said, I do still use them, on occasion - but only when lowering immersion doesn't bother me. That is generally going to be 'montage' moments where we don't want to role play the details, and the ramifications of success and failure have only short term impacts on the game. For example, rather than walking through how the PCs explore a carnival and all the games there, we may do a skill challenge to see how they did at the games while trying to gather information on where they can buy magic items.