Well, it depends. I think one of the most sensitive to water quality would be SPS. But that also depends if you have enough lighting and water movement. When you get to the harder corals to keep, it is not only water quality you have to worry about, a lot of other factors come into play.
And I think you can even keep SPS without water changes if you dose for calcium and alkalinity and magnesium. With a mature reef, you can get away from doing water changes if you don't feed a lot. You will get into trouble as you increase your fish bioload. Especially fishes that poop alot.
Also, long term, you may run into old tank syndrone if you let your tank get filled with detritous. It will slowly overtake the amount of nutrient you can biologically filter.
And I think you can even keep SPS without water changes if you dose for calcium and alkalinity and magnesium. With a mature reef, you can get away from doing water changes if you don't feed a lot. You will get into trouble as you increase your fish bioload. Especially fishes that poop alot.
Also, long term, you may run into old tank syndrone if you let your tank get filled with detritous. It will slowly overtake the amount of nutrient you can biologically filter.