I am not sure that web search is a monopolistic market, though it seems that Google is the dominant player. Google itself wasn't the first player, and managed to capture a large market share from established incumbents. Why do you think that competitors couldn't quickly capture the market? You seem to think this is an obvious fact, but I don't see why, as switching costs are very low.
It seems to me that the important market is online ads (which is where other companies focus), and that Google is the only company willing to invest in web search.