Once you get a good grip on the Americas, provided you don't expand too fast and crush your economy with colonial maintenance, you'll have more money than you know what to do with. They don't shine because they start with 1000 people + whatever natives you didn't kill in them, so they don't have the people to produce lots of trade goods or taxes. There are a ton of provinces to control in the new world, and I think that's the main thing. There are maybe 20 provinces just in the bahamas that you don't need to make war over.
It's been a while since my Castille faceroll where I took over all of America, but I distinctly recall setting up lots of centers of trade and concentrating on being mercantilist, since I controlled something like 3/4 of the worlds sugar and tobacco production. I basically withdrew from all the european wars and crap after I formed Spain and concentrated on securing the Americas, before pushing into the Pacific from the Americas, and the Orient from South Africa and Zimbabwe. I know, I know, Castille is easy mode, but the lesson is the same. You can choose to go 'isolationist' at least in respect to Europe and accrue a lot of money and territory without a whole lot of wars. I think you can go the other way too, but it seems like more trouble.
Keep in mind that you find new resources at your colonies which means you can find new gold mines. I think there are only something like 5 gold mines in all of Europe, most of which are tied up in HRE crap that makes them problematic to conquer. The exotic goods like sugar, coffee, etc. also are worth quite a bit, due to the rarity of provinces that produce them in Europe. Early on, you're going to have such a small population in the places producing these goods that the money won't be particularly noticeable, but over time the investment pays off.