So I guess that what I like is the idea of it, the purpose behind it and then to make it my own by giving it my personal flavor. I love the idea of a structured non combat scene where everybody must participate toward the same goal instead of just relying on the character better suited for the task. I love the initiative structure since it guarantee that everyone will get under the spotlight. I love to see players get the most out of their skills by using them in uncommon ways, they always surprise me with a way to use a skill that I did not thought about. I think that Skill Challenge really push and reward the creativity of the players instead of just going for the obvious skill. And again, it 100% go toward the philosophy of 4e that everyone is equally important to the success of the team, it makes the players rely on each others.
Pretty much this... but what I've found is that if the situation is created correctly then it naturally flows into multiple PC's dealing with different facets of it. I think there's a section in Xanthar's where it talks about how to design complex traps where multiple PC's/skills are involved and I think it's just extrapolating the advice and examples given here to other situations in 5e.