In fact, a market without noise traders will tend to break down, because prices in such a market will become fully revealing. Informed traders will not enter a market without noises, because it is impossible to profit from trading in a completely efficient market. Informed traders need the existence of noise traders to “hide” their trades and by trading on their private information, informed traders make profits. Through trading, informed traders gradually release relevant information to the market prices and together with the noise traders, they help bring the market back to equilibrium.
Some Behavioral Finance articles point out that the risk generated by noise traders can lead to limited arbitrage: thus, the presence of noise traders undermines the classical no-arbitrage reasoning. However, whether noise traders can survive in the long run, and if they can, how much of a pricing distortion they create, are still open questions.