Usually the biggest concerns of a slow chill are....
DMS (cooked corn flavor) is created from SMM when wort is hot. DMS will form until below 140°F (60°C). SMM is boiled off during boil, it's why we do an open lid boil. SMM has a half life of 37 minutes. 90minute boils usually reduce SMM levels below the perception threshold.
Unwanted bittering late addition hops (less than 45min) continue to isomerize until wort drops below 175°F (79°C)
Infection bacteria love warm temps. Below 160°F (71°C) (pasteurization temp) the wort is at risk of infection.
As far as adding cold water to chill, this could be very effective at dropping the wort below those critical temps very fast. But I would make sure the water is sanitary or sterile (pre boiled, chilled, sealed)
As far as the last 10°F(~5°C) allowed to slow chill. It's a common practice with few side effects other than risk of bacteria taking hold before yeast gets going. It may in some cases delay your pitch and add to the overall brew to glass time.
Update: forgot this initially.
Chill Haze when wort cools slowly this allows certain proteins to remain suspended resulting in chill haze. The thermal shock of a rapid chill of the wort causes them to drop out. Usually have to drop below 80°F (27°C) within 15 minutes for sufficient thermal shock. Chill haze is identified in finished beer by being hazy when cold but then gets clear when it warms up.