Theres a few reason's that come to mind.. Other than they are ugly, stupid, and incredibely common.. Heres some that I can think of..
1) Water Quality issues.. Goldfish tend to release alot more Urea than other fish, especially the man-made 'Globoid' shaped ornamentals. If you think about a fish's body shape in the wild, each fish through evolution has evolved it's body to best fit it's environment. Ornamental goldfish had no choice in their body shape, so they must expend more energy in order to swim and compete for food. This creates 'Metabolic waste' which is similiar to a human sweating. Ornamental Goldfish simply put off an extraordinary amount of waste, which can be detrimnetal to a number of ammonia sensative tropicals. (The higher the temp and pH, the more toxic Ammonia.. Hence, Goldfish living in a cold water, low pH bowl is non-toxic.. in hard water in a warm area, its quick death..)
2) Water Temperature.. Sure, you can find a happy medium in which both fish can live happily. Most fish are adaptable to temperature, so I am not going to say they wont 'Thrive' without the temp being perfect. One thing you need to keep in mind, however, is that the increase in temp will increase the metabolism of the goldfish, thus creating more metabolic waste. Sure, alot of Goldfish sites reccomend a higher temperature to aid in digestion, but at the same time these websites also are adamant about keeping goldfish in a species only tank, which is often VERY UNDER-CROWDED. (1 or 2 per 55g)
3) Disease vulneribiltiy.. Most Ornamental Goldfish are captive bred, so the disease you might see in them should not be specific only to goldfish. However, these captive bred ornamentals have never had the exposure of many of the tropical diseases that you see from wild-caught fish. A wild-caught South American fish, that could be very tolerant to a specific disease from it's native waters, might be a disease courier for a vulnerable captive bred ornamental species. Think: Native Americans + European Settlers.
4) Aggression.. Goldfish are notoriously stupid. They are very easily picked on, and their fins can be tattered quickly by nippy fish. Although some fish just ignore the goldfish, it is likely to happen eventually. I am always surprised to see healthy feeders grow up with predators, as I would assume their fins would get shredded. Also, goldfish are big algae grazers with a big appettite.. If you take certain precautions to get extra peaceful species to co-habitate with the goldfish, they might just acquire a taste for slime-coating and stress the peaceful tropical fish..
Just a few of my thoughts on the issue.. Like others said, I find it un-natural and pretty much annoying when I see this happen.. As if It's a waste of valuable bio-load space that cuold be used on a fish with a brain bigger than a grain of sand. Did I mention they are stupid and ugly? Ah well, it's just an opinion!
) and it died before summer was out. 
Very informative explanation, Miles.
