Plants on Earth play an incredible optimization game. Water is necessary not just for chemical metabolism, but because throwing it away is an essential part of the internal material transport systems of a plant. Evaporation in the leaves creates a relatively lower osmotic pressure in the higher levels of the plant. Between capillary action and the slight but insistent pull to replace evaporated water in the leaves, plants have a pumping mechanism with essentially nil energy input: minerals and nutrients gathered in the roots just ride on up with the tide.
Stars may be a similar story for efficient fusion. Sure, with sufficiently advanced technology, I can make inordinately denser energy sources with less boil-off. But do I want to? Maybe letting the brute physics of a gravity well do the job simply has unbeatable efficiency -- just like evaporation as one end of a pump for plants on Earth is clearly no comparison to any motorized pump for volume, but for cost-effect, nothing else comes close.
Stars are just so wasteful; all that energy going into convection currents, and you have to build this big damned sphere to capture all the energy. Better to lift the damned thing and, at the very least, make a dwarf star out of the larger ones. Now you're talking trillions of years of burning (it's still a trash fire, but at least it's manageable).
But what if we need/want volumes? The way we can't (or don't want to) use trees/plants for pumping water in time-efficient manner, we may not (want to) use the gravity brute force based stars as energy sources and we may invent more time-efficient fusion reactors.
You're probably better off disassembling the suckers and storing their matter in a sensible way, rather than have it sit there, burning. Stars are kind of like trash fires; maybe we should be looking for less energy in a type III civ, not shielding.