Earlier quoted context omitted.
This is an interesting idea. Although if anyone has enough money to single-handedly move the market price, it devolves into a dictatorship of that person.
Robin Hanson has a paper where he argues that such attempts at manipulation won't work: https://mason.gmu.edu/~rhanson/biashelp.pdf Based on the abstract, I think the essential argument is that a market manipulator acts as "dumb money", attracting "smart money" who are happy to profit by bringing the market back in line with reality.
Take the inequality example that you mention. Reducing inequality might require large government spending, like free higher education, or extensive government-provided healthcare. This requires funding which pushes up interest rates.
Someone in the prediction market might agree that free higher education reduces inequality but might also think that it will increase the government’s cost of financing its spending. The latter is what usually gives politicians trouble with financial markets. How would a prediction market resolve this issue?