Consider how the reasoning proceeds if we do not take solving a problem as a Boolean. Also let's measure not just by whether the problem exists or not (or to what degree) but also by how much overheads or missed opportunity the society is having with the institutions even just existing.

In the scenario A, knowingly or unknowingly, they would tend to solve the problem partially. The others around would see their contributions so far and foresee their value for the future. If others discover or perceive that the institution is not holding any promise for the future, the institution could struggle to survive.

In the scenario B, the institution existing is entirely a lost opportunity for the society.

Hence the scenario A is typically better (for making progress with given amount of resources).

In scenario A, the problem is already solved, and the institution exists to prevent that solution from being implemented. That's the whole point of this comment thread.

Surely that is not better than lying about an imaginary problem?

>> In scenario A, the problem is already solved, and the institution exists to prevent that solution from being implemented.

In my understanding, that's one way.

Another may be to keep making slow progress to solving so that those around see the contributions and the relevance of the institution but not fully solve.

Another way may be to show their relevance even if the problem is not getting solved by convincing that the situation would be worse without them.

And so on.