Making beer is all about controlling variables: quality of ingredients, temperature, sanitation, etc. Using ice to chill is obviously a method employed by many people, and with success. The two problems that I see are 1) contamination (which has already been extensively covered), and 2) the inability to do a full boil, which is important to me. I just use an entry-level copper wort chiller, and am fortunate enough to have 55F well water to do the chilling.
I was invited over to a brew session by an acquaintance, and he & his brew buddy use ice to cool partial boils. At that time, they were having no trouble. Suddenly, within the last few months, they've thrown out three batches. They haven't found the cause yet, but given my observation of their techniques, there are several things they need to eliminate as possible causes, and the ice chilling is one.
If it fits your setup and schedule, I think no-chill may be a way to go, although I haven't tried it yet. There is a huge thread on no-chill brewing; it is practiced a lot by Australians, and there seems to be a growing contingent in this country that is trying it. Personally, the idea of brewing one day and not being able to pitch until the next kind of bugs me, but given the fresh water situation that already exists in some parts of this country, and the crisis that is predicted, it may be the way of the future.