Depends on where you are, I guess. I had a massive silver maple at my apartment house when we lived there that was dropping limbs like it was going out of style. I called them up since the thing was arching right over a power pole - they came out and wanted nothing to do with even limbing it. Couple weeks later the tree was rubbing on the pole during a windstorm, caught fire briefly, and blew up a transformer up the street. ...they continued to do nothing with it. The adjacent property owner had to fell it as there were too many customer complaints of car damage due to dropped limbs in their parking lot! This was right before western mass electric sold to eversource, so that may have had something to do with it. Eversource has been pretty aggressive with tree removal.. I often follow the orange truck of love (Asplundh) and pick up their leavings after consulting with property owners.
The heavy cable in the sycamore is telephone. It is large enough that it is probably serving 50 to 100 separate telephone lines. My guess is there is no way they would even think about moving it to make your life easier. That enlarged plastic thing about a foot long is where they would connect individual customers to the main cable. Inside it, the cable is laid bare so the telephone installers can get at the inside and connect to a specific conductor pair. I did that stuff for a living back a long time ago. If you look closely, the large diameter cable is being held up by a skinny steel cable that it is strapped to. You can see both separately on the left side of your second picture.
It'll end up ash if he can figure out how to get it down Sounds like it is just gonna depend on your local phone company and their policy on tree trimming. I know around here the power company is a lot more aggressive with trimming trees than ma bell is. Shouldn't be too hard for your skilled tree cutters to drop that suckah without so much as a scuff on their precious wire. Even if it gets damaged, it should be less of a problem than the Sprint trunk line we had to dig around a few years back. They sent a guy out when we called in the UPS dig ticket, we asked who to call if we hit the cable...he said our bankruptcy lawyer...and not to worry, if we hit it there would be a black helicopter on site post haste!