A perfectly efficient market would give nobody a reason to trade in it
Sanford Grossman and Joseph Stiglitz pointed out a catch in the idea that market prices instantly reflect all available information: if prices already told you everything, nobody could profit from researching a stock, so nobody would bother researching it — and prices would stop reflecting new information at all. Perfectly informationally efficient markets are therefore impossible; some inefficiency has to survive to pay the traders who keep prices accurate.