But the more crackpoty things...yeah.
Things like "the Ancient Egyptians came over to America to mine copper" require that said Egyptians were able to sustain an expedition over here with not-terribly-seaworthy ships (Mediterranean, yes, Atlantic, not likely) while ignoring the fact that they could buy almost all the copper they wanted from local sources at vastly cheaper rates (once you take into account how much everything costs, including the time and labor of your miners), and managing to keep all the evidence of their passage hidden. While it's not impossible that some power-mad and paranoid entity decided to have an expedition to have a secret source of copper in case the Cypriots and other sources turned off the spigot, it's really, really, really, really unlikely.
OTOH, Thor Heyerdahl's Kon-Tiki expedition proves that you can go quite a ways on some nasty seas with a pretty rudimentary ship (as such things go.
While you're absolutely right that extended periods of trade (say, more than a couple of decades worth) were extremely unlikely, I'm not ruling it out entirely. Never underestimate the power of humanity to convince itself that something completely unnecessary or overpriced is quite desirable.
Mined copper might just have been the secondary cargo...there may have been a quite lucrative trade in the feathers of exotic birds from South American rain forests.
(Yes, I know none such have been found, I'm just using that as an exemplar of a rare good that might make pursuing such trade more likely, despite the costs.)