The Brits knew how to do these things. When you want to milk a country dry, you co-opt one native group and train them up as the middle management. You stay on top but aside from the occasional civilian massacre you do little more than sit and collect the taxes and extract resources. You justify it all by saying you're bringing the fuzzy-wuzzies civilization, or you're protecting them from the bad old Russian bear (German eagle, Yellow Peril, whatever). And you let the hate-pinched-faced old maids hand out Bibles. Every once in a while one of them will get strung up and then you can declare a revenge war against the "threat to Christianity and (sniff) motherhood" and gas a few thousand malcontents. Meanwhile, the trade lanes to India stay open and the money keeps pouring in.
We're getting there. Our model is different from the Brits primarily in who gets the goodies. The Brits poured a lot of it back into the Empire. We're putting it into private pockets. So far the rubes haven't noticed, but ours is an inherently more risky business model.