I could imagine humans fighting over the limited energy harvested by Sol’s Dyson sphere in 10million years. It would give any group of human’s controlling it a massive advantage, similarly to the advantage having the only A-bomb gave US briefly.
Higher technology levels have only increased the efficiency of our power use and use per capita. I'm not saying we're at the height of technology or development or anything but the idea we'd need a whole star's worth of power output for something I think is ludicrous.
If you've got the technology to build a Dyson sphere (or swarm) it's unlikely you'd actually need to. To even get to that point as a tool-using civilization you couldn't have had unchecked geometric growth. Unless you had some Motie-like biological imperative to reproduce uncontrollably your civilization would reach a point long before Dyson sphere level where it worked fine without having to move the mass of several solar systems around a star to capture some high fraction of its power output.
Who am I kidding, they would still fight over it...