Lots of "yep".
Well, let's slow down a bit. We'll keep the pillar abstraction, but recognize that it is just that - an abstraction.
How much a character had built-in buttons to push to interact with a given abstraction is a spectrum, not a yes/no modal toggle. Further, as I've detailed elsewhere (and may try to find), built-in buttons are not the only way to interface with a given pillar. McGuffins are perhaps the most commonly discussed external power source, but far from the only one.
As I've said before, if the party has literally 0 ability to interact with a pillar, that represents a complete and utter failure of everyone involved - GM, module writer, world-building, system writer, etc.
But, yes, sometimes, the party doesn't have any built-in buttons to push. And that's when the game gets interesting!
My BDH party? Unless it's innuendo, none of them should be allowed anywhere near the "social pillar". They generally struggle to convince the people that they're saving that they are the lesser of two evils (while gleefully wading through their opponents like they were human). And that's part of what makes that party fun - they struggle with things that anyone else would breeze through without even noticing.
No, IME, it forces them to get creative. To interact with the world, the NPCs, anything that they can to gain some advantage. To… basically play (my understanding of) Fate, and stack advantages / aspects / whatever, until they've given themselves enough advantage to complete the challenge. Or to redefine the challenge into something that they *can* handle ("well, we can't find him, but maybe we can make him come to us", for example).
Parties with these weaknesses are the best.
Actually, I was saying that Reed should sit out, and let the mass army Hobos solve the problems that he, conceptually, should be best at.
That's more the model I prefer.