The goal of a prediction market is to be able to forecast the future as accurately as possible. Restricting informed traders weakens the mechanism that makes them useful.
Money signals how strongly someone believes something will happen.
Like, if I know a month ago that the US will invade Iran, and I make a big bet on "Yes", then that of course gives people information, which in turn negates my edge. So it's entirely self-defeating. It's actually way better to try to convince the general public that it won't happen through non-market means, or perhaps even buy a few "No" shares just to drum up public opinion. You'll get that money back anyway once the bet resolves.
Just imagine: the boxing champ is planning to take a dive in the third round. You think he'll make his bet a week in advance?
Please look at the name again. It's "prediction" market. So if you have credible information before resolution, it's no longer a prediction.
Also your premise is incorrect. The goal of prediction market isn't that. It's to represent wisdom of crowd. Informed traders who can influence the outcome are no longer using any wisdom, nor they're part of the crowd.
Yes prediction markets represent "wisdom of crowd", and they do this by rewarding people who contribute correct information. So informed traders are the ones making the system work, and they're putting actual money on the line to back up their claim. Without them you're just left with uninformed guesses, which isn't really "wisdom of crowds", it's noise.
But if you're defining an informed trader to already know the answer, then it's problematic. I hope you see that as well. The market should reward some logically deduced conclusion, not power. That's my position.
Also it's not noise, an average trader is not choosing a random number between (0,1). They can do research and their guess can be informed. Hence, the use of word wisdom. By your definition, this is gambling then.
If the goal is to produce the most accurate forecast possible, then informed traders (especially asymmetrically informed traders) are a feature of the system, not a bug. The market is a system for discovering the truth, and it generally rewards whoever brings that truth to the table first.
If the goal is to create a fair playing field where the crowd collectively arrives at an answer, then yeah someone with private information becomes problematic.
But I'd argue that's optimizing for fairness at the cost of accuracy, and accuracy is much more important.