Why do phone and cables companies leave their cables behind, and what to do about it?

They do it because they can.

It costs money to remove cables. If the municipality doesn't require them to do so, why would they? Most people don't notice or complain, and there's the off chance they'll use it again if the next owner wants service.

I've gone so far as to cut them free of my home, neatly coil the cable, and wire it to the pole on the alley. Eventually they'll be at the pole for some other reason and cut it down. Technically the cable may be their property, but that doesn't mean it has to lay around on (or over) mine.

Two possibilities :

• Other Company

If I have fiber and switch to cable (or vice versa), the cable company will remove the fiber from my house but they will leave it at the pole because it is the other company's property. Or they may let the other company...

• Save for the next customer

If I move out, the company might disconnect but leave at the pole because of the next tenant or owner wants similar service then they can use the existing cable and save $.

But in any case, as stated by Harper: if the wires are near the ground, don't touch. Call the electric utility (they normally own the pole) and they'll check it out and remove, repair or notify another utility as needed. Even if a cable really is low voltage "nothing", things can get messed up at the top and make it hot. One time I had a low hanging coax situation. Called Pepco and they took care of it even though I knew it was comcast and knew that 99% certain I could have climbed on a ladder and done it myself. The 1% risk is a serious one.

Downed wires are downed wires! STAY THE HELL AWAY

You are talking about a wire which comes down from the pole and comes near the ground. That is a "Downed Wire". They are dangerous as all getout, because they can have live voltage on them.

You should not even be close enough to tell if they are cable TV vs phone wire! STAY AWAY - STAY ALIVE.

Even if they were telecomm, you have no idea what they are attached to (or what they got tangled up in) on the other end. Technology changes are obliging phone and cable companies to fit powered equipment on the poletop, and having to take whatever power is available there, be it 240V, 277V or 2400V.

I do work on overhead lines from buckets and towers. The golden rule of not getting dead doing that is that the bucket/tower lives in "poletop world", and that vs ground world is matter vs antimatter. Nothing ever, ever is allowed to drape or be let down from "poletop world" to "ground world".

Call the power company and report a downed line

Pardon the sarcasm, but it illustrates the point: "Before you call us, step really close to the wire and see if it's phone line or coax" said no power company employee, ever. That would be a deranged thing to tell the public, because sooner or later one would turn out to be energized.

The PoCo will come out and deal with it, with extreme prejudice.

If it is indeed a telecomm line, they will remind the telecomm company of the terms and conditions of their lease of space on the pole. And maybe send them a bill for the service call. So, profit center for the PoCo lol.