A flaw in the GDP

When I was in economics class last tuesday, the topic of net exports and how it affects the GDP and the economy came up. I seem to recall my economics professor, whom I have great respect for by the way, say something like this:

"What happens when the value of the dollar goes down?"

Student: "uh, it increases exports?"

"Yeah, because more foreigners buy our goods, and that's a good thing."

For those of you who don't know, net exports (exports - imports) is one out of four factors used to compute the GDP. So if exports goes up - or imports go down, or both - the GDP rises. So the logic presented is that if the value of the dollar goes down relative to other currencies, the volume of exports will rise because foreigners can buy the same amount of dollar goods for less of their currency and imports will go down because we can buy less of foreigners goods with the same, weakening, dollar value.

This is true. The problem, however, and the reason that devaluating the dollar is not beneficial to the American economy even though it boosts the GDP, is that foreigners buy more of our goods because they get a better deal on them, and we get a worse deal. Whereas if the dollar is 1 to 1 with the euro we can get a euro for only 1 of our dollars, but if that ratio is 1 to 1.5, then it takes 1.5 dollars to get the same thing. We're worse off, they're better off.

This is another example of how the GDP can be wildly unreliable when it comes to measuring the true state of the economy. I don't contend that we should eliminate the export/import part of the GDP equation, nor could we viably switch it to Net Imports (imports - exports), merely that one must be wary of this statistical unit and realize that it leads to imperfect conclusions, even if one does not have a viable alternative metric.