You definitely can invest in USD/Euro. That is what people do on forex...
No, you don't invest in USD/EUR pair, you speculate. Forex trading is a zero sum game. My point is that Bitcoin does not reliably produce wealth, it is a currency, similar to speculating on forex.
At some point, user numbers will reach saturation, and Bitcoin will no longer produce any returns (except maybe due to deflation).
The bolded part is key. Right now people are investing (call it speculating if you want) in the prospect that bitcoin is not at its saturation point and that it will continue to climb to some saturation point. That is an investment as surely as is someone putting money into a startup company. It is a high-risk investment, but an investment just the same. When bitcoin does in fact get near and/or reach that saturation point, then your comparison to trading USD/EUR will be accurate.