I often take a more transparent style to the same approach: "We can't think of any good solutions, so here's a possible, but obviously flawed solution to talk about. Maybe it'll inspire something better."
People generally don't like to propose imperfect solutions because of the fear of looking dumb and wasting time. But, when everyone is stumped, sitting in silence is wasting time. Re-igniting the conversation by saying "I don't want to actually do this, but here's another angle" can kick the problem-space search out of a local minima.
I call this "proposing a strawman solution". I don't know why it works, but it frequently does. I think that doing a long search for The Perfect Solution is akin to premature optimization. Changing focus for a while seems to help.
People generally don't like to propose imperfect solutions because of the fear of looking dumb and wasting time. But, when everyone is stumped, sitting in silence is wasting time. Re-igniting the conversation by saying "I don't want to actually do this, but here's another angle" can kick the problem-space search out of a local minima.