Wouldn't it be a more balanced approach if the technical problem were presented on the spot to __all__ interview participants, not just the candidate?

It's a technical job, it must be a collaborative effort in finding solutions! Aren't we looking for a team member, not a lone-ninja.

Sure, the candidate has to be more vested in advancing the process, but the fact that there's no known-ahead answer would potentially surface not only technical skills, but also personal ones, and ... at both ends of the table.

Not to mention, the "house-experts" could find such sessions stimulating, to say the least... Imagine, you get back to your desk after interviewing a candidate, and your team mates ask you "so what was the tech problem this time?", "could you crack it?", "did he/she crack it?".