Knowledge acquisition goes through the roof
Science fiction writers would be very valuable because their imaginations are quite strong. Imagining if we can build an FTL spaceship will quickly yield an answer. Questions about how to build that FTL spaceship will also yield immediate answers. This pattern of imagining "can I do/build/see/experience this thing?" will have a lot of unexpected results.
Relieving scientists and engineers from the burden of experimentation, gives them far more ability to rapidly acquire knowledge. It would be golden age. An example of what this might be like how Sparks operate in Girl Genius. Their fanciful inventions just work, the first time, all the time.
Zealous but stupid terrorists will have the plans handed to them on how to carry out the crazed musing of their inner demons. If it's not possible to achieve their goals, they may give up or they may just go out in a blaze of glory. Or, they'll hunt around for new goals that are possible and execute those.
Religion often makes assertions about how the world works. For the most part, these claims aren't verifiable but with imagination-based precog, they are. Say a Muslim terrorist dreams of 72 virgins then finds that the dream is impossible. Does he keep fighting? A Christian dreams they will go to heaven if they give away all their money. Now they know. A Buddhist dreams of meeting Buddha and finds that's impossible, what then?
Knowing that something is possible is a huge motivation to go do it. The movie "Meet the Robinsons" is an excellent illustration of this principle. Once something can be done, it's easier for other people to follow suit and duplicate it.
This is ability is Worldbuilding in real life with a perpetual reality-check tag on it.