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.
A better roof covering material is stainless-steel.
Then 430 has less thermal expansion than 304 but 430 is more risk of crevice corrosion. Or 444 has about the same thermal expansion as 430 but has a smaller risk of crevice corrosion. Basically, 430 can be bent to shape one-time but not worked to shape. And 430 shouldn't be cut with a cut-off disk but should be cut with machine tools.
Stainless-steel is not painted but AK Steel has a pebble-finish in 304 and 316 for roofing. The pebble-finish has a dull finish. Otherwise, a #8 mirror finish is not possible for roofing, a BA finish is still too bright, while a #4 brushed finish might be possible.
The stainless-steel sheet-metal comes on coils and is sold wholesale by the pound. Stainless-steel by the foot would be fabrication and would be very expensive. The stainless-steel sheet-metal can be formed into standing-seam panels with a portable standing-seam forming machine.
The roof covering can also be done as side-lapping lateral-strips taken straight off the coil. A roof covering like this uses thicker material, at 0.028" to 0.030", but lays flat on both course side-laps and section end-laps. However, lateral slots must be cut in the stainless-steel to allow for thermal expansion at the attachment and the stainless-steel must be attached with stainless-steel nails or wood screws. In fact any metal touching the stainless-steel must also be stainless-steel. Gable-ends either need a stainless-steel square-tube over-the-roof hold-down or the roof course-ends need to be cabled down to brackets on the gable-end. Ridge pieces are bent in a brake from pieces that have been cut-to-size and flattened. The ridge pieces reach to overlap the sidelap so that upside-down machine-screws can attach the ridge piece to the top layer of the sidelap. Now section end-laps can't attach to other section end-laps and ridge-piece end-laps can't attach to other ridge-piece end-laps because the thermal expansion would be working against the end-laps.
The lateral-strip side-lapping stainless-steel roof-covering will hold rainwater for a couple of hours in the first 1/2" of the side-lap. Also, the side-laps make a slightly ventilated roof-covering while the stainless-steel itself tends to reflect solar heat. A high-end house is more likely to use standing-seam panels while a do-it-yourself build is more likely to use this side-lapping lateral-strip method.