I see with some high end housing construction the use of copper for gutters and drain pipes as well as roofs and flashing. Is using copper where it will be exposed to water runoff from rain a good choice? Will the copper oxide dissolve into the water and create copper pollution wherever the water runs off to? What about longevity, is copper a long lived building material solution? If copper is not a good choice due to durability or pollution, what are some better options that a high end house might be built with? Aluminum, galvanized steel, etc.?
Availability in the long term
You didn't include in your list a mention of how available copper will be in the future; this matters, for sustainability, because we can't afford to be using it for guttering if we're about to run out of copper ore. It is a very important metal for other purposes, such as electrical components.
Wikipedia has a good article on the concept of "peak copper" which does make it clear we have a pretty good reserve of it still, despite a prediction in 1924 that it will soon run out and "Our civilization based on electrical power will dwindle and die".
For guttering, the price of copper does matter, because if it becomes expensive it becomes highly desirable to steal. This already happens in New Zealand with copper hot water cylinders occasionally. The risk of theft is also heavily dependent on location, culture & local law enforcement of course.
Apparently copper is anti-microbial but stainless steel is not. I'm not sure about other metal options for guttering, such as zinc galvanised steel (zinc is mentioned at the same link as being anti-microbial). Even if the copper itself is safe, in some cases it may be healthier to have the microbes present (it helps us build immunity).
I'll leave the longevity & pollution aspects of the question to others who know more about that side of it.
Copper for such a use could potentially be a health risk to those succeptable to things like hepatolenticular degeneration. This depends on how much copper is already present in the soil, what type of well is being used, whether the water is being treated before consumption, and many other factors. Sustainable though? Might depend on what the chemical makeup of your rainwater is. Where I'm at, it would react rather quickly. Some people like patina though.