I don't know where you get the impression that a DM has to ignore the rules
Possibly from the rulebooks themselves? The ones that say that you are meant to set the skills that can be used in advance? Possibly from the skill descriptions that say what the skills actually do?
Yes, it is good when planning a skill challenge to set it up so that a wide range of skills can be used (just one reason skill challenges are not complex skill checks). You'll also note that one of the possibilities for secondary skills is that they don't provide a success towards the skill challenge - just a bonus to subsequent skills.
I know Skill Challenges are sort of Rorschach blots as far as 4e goes, because they're really open-ended, and I'm sure DMs do lots of different things with them. Still, I think the DMG quote above is pretty clear about what the intent is: everyone should contribute equally to a SC. And that's the thing that causes the problem.
And I think that you've committed the fallacy of the excluded middle there in misreading the intent of the DMG. The goal of skill challenges is that everyone should be able to contribute. And that people should be rewarded for finding creative methods of using skills that would not normally be relevant.
What causes the problem is DMs neither using the rules as written (which, in the initial example, don't allow Intimidate to be used on a persuasion skill challenge, instead making it an automatic fail), nor the rules are intended (which very much intend the GM to use common sense about what is plausible).
I think the risk is less about the SC primarily, and more about the mindset that lead to that being considered a good idea. If everyone needs to always contribute equally,
If everyone needs to always contribute equally then we are in the land of
Harrison Bergeron. We wouldn't have roleplaying statistics - all statistics would be exactly equal. We
certainly wouldn't have the fighter with three skills, and the rogue with six while the wizard has
Ritual Caster. The idea that "everyone needs to always contribute equally" is nothing but a straw man and I wish people would stop making this blatantly obvious straw man because it undermines any belief I have that they are both discussing things in good faith and have even the most basic understanding of what a character sheet, skills, powers, and attribute scores actually are.
What 4e has is the idea that everyone needs to be able to
contribute. That there should always be something constructive that they can do, and the best plan shouldn't be for the rest of the party to just sit down and keep mute while the bard is talking. This in no way means that the bard isn't the star of the social interaction.
What it means is that, to use an analogy, the bard is the lead singer in 4e for that specific song and the rest of the party for that period are effective backing singers, drummers, or guitarists. In more normal models the bard would instead be a soloist where the best thing the rest of the party could do would be to sit down and shut up rather than join in the improvised jam and possibly produce some excellent riffs of their own.