The overwhelming success of free market provision of just about every good and service, vital or otherwise, is one of the most obvious facts about the modern world. That's all there is to it. Incentives work. Everyone knows this; it's no good pretending otherwise. Even the radical left (outside of China and Cuba) is too embarrassed to make a general case for socialism anymore. This is why the left pretends to favor markets in the abstract, but then claims that they are concerned about specific problems. It's not the market per se, it's "corporations", or specific corporations. They're not against private supermarkets, but they are against private doctors. They're not opposed to private colleges, private car manufacturers, or private housing, but they are opposed to private primary schools. They're not opposed to a free market, but they are against tax cuts on various spurious hypertechnical grounds. Etc. It's a pretty pathetic legacy for a political and economic movement that used to be so bold as to suggest that command economics would lead to greater growth and prosperity than an unregulated market. That water should be kept out of the hands of a private provider is just the latest in this tired series of tricks.
So, at any rate, the advantages you claim not to see in private water distribution are the obvious, familiar, and well established ones. We can expect greater supply, greater service, etc., in a market in which private providers compete to provide water as compared to centralized distribution. Just as we do in every other area with which we have any experience, as everyone knows.
Having said this, it is worth mentioning particular problems with water distribution. One is that a fixed delivery infrastructure is expensive, and perhaps not amenable to competitive installation. Perhaps. We had private railroads in the U.S. for many decades, each of which would build expensive rail infrastructure. We have competitive phone companies. So it's not clear why we couldn't have competitive water delivery. (We have competitive delivery of fuel oil and drinking water already, notice). I see no reason to conclude a priori that water distribution is a natual monopoly. Admittedly, if it were, there would be reason for stricter regulation of it (like cable T.V. or local phone). Even still, this isn't an argument against privatization, exactly. It's an argument for monopoly regulation, perhaps.
Poor countries have a host of problems. Poverty is the cause of them. That poor countries have, sadly, dirty or inadequate water is hardly an indictment of private provision of water. You might as well claim that famine in the most miserable areas of the world shows that the government should seize and operate grocery stores in the U.S. The phrase "global corporation", thrown around like some contemptuous epithet, doesn't provide any more power to your remarks, your expectations to the contrary notwithstanding.