Usually, with the help of a neighbor, we would take down the dead stuff ourselves using several of the ideas already mentioned. I was a telco lineman and would sometimes use my gear to climb when necessary. Too old to fool with it now though.
Around here, dead trees or branches, in the vicinity of a power line, are removed by the local utility company at no charge. There are exceptions though. I had three dead white pines, all over 150' tall, along my private road. The trunks were 36" in diameter at the base. If one were to fall on the adjacent power line, it would surely break off one or more poles and take down the line itself. I called the power company but they refused to remove them. No way was I going to mess with them myself.
Fearing an extended power outage, I called a tree service. There's only one in the area, and they won't touch them either due to the proximity to the pole line.
Over the years, two of the three trees came down on their own and luckily, fell back into the woods, away from the power line. The third is still standing and I'm keeping my fingers crossed.