I've been thanked by every processor I've ever used for bringing my deer to them "so clean". Unless it's getting mounted, I cut through the sternum and always cut through the pelvis. My deer get sprayed out and very seldom drug anywhere after being gutted. All the deer killed on our property are drug out, guts intact, to a location far from any hunting spots. They're gutted there, then transported by sled/ATV to the hose, then hung up to drain before being taken to the processor, or quartered and hung in our meat fridge.
There's no real right or wrong here, it's situation dependent. Frankly, I'd rather open up both bone structures and know I got everything, than skip that step for fear of a few leaves. If I had to drag one a mile through the woods, I might think differently, but in nearly every situation I find myself in with a dead deer, I'm opening them completely up.