Agreed except for foreign income: we have treaties with most countries to avoid double taxation: If I've paid taxes to Turkey for money earned in Turkey, why do I pay it again in the US?
Now, things get more complicated with foreign investments. If you've paid taxes on the investment in Ireland, you've likely paid less than you would in the US -- so that doesn't quite work. That's where things get complicated.
should all work like multi-state commuter taxes--i live in NJ, work in NY, and my NY tax is credited against my NJ liability (leaving no liability to NJ, as NY rates are higher (at least with the extra NYC tax thrown in)). tax treaties (as exist between many states) just make the revenue sharing easier from the governments' point of view.
Now, things get more complicated with foreign investments. If you've paid taxes on the investment in Ireland, you've likely paid less than you would in the US -- so that doesn't quite work. That's where things get complicated.