You basic stantard POTS (Plain Old Telephone System) is a pair of wires that run from the nearest substation building to your house. One wire, just for you - if that wire is not interupted (cut or grounded) then your phone will keep running. Odds are, too, in a larger urban area, the trunk lines between the substations are now fibre buried undergrund, so if your neighbourhood line is not down, the phone system stays up. If one trunk line dies, well, the phone system like the internet is often configured with multiple paths and flexible routing for problem recovery.
The phone cable provides enough voltage and current to power a basic touch-tone phone. The central substation has battery-backup to support this during blackouts.
Phone lines, being a collection of dozens of tiny thin cables, are usually strung with a strong wire messenger cable to hold the load and tension. Not sure about power, but I doubt tying a big power line to a separate bare metal cable is ever a good idea.
Power, OTOH, is sort of like the water distribution system - one big feeder cable feeds an area, where it is then dropped down to 220V (whatever) at a transofrmer, and each house in the area is fed with a tap from from that same wire. SO any interruption anywhere in the system stops feeding the whole area, just like a broken watermain could mean no pressure for the whole neighbourhood.
Of course, large distribution points are fed by high voltage lines from multiple sources, but in a difficult time, if one or more feeds goes down, it may overload the other feeds. Since they will be breaker-protected from excessive load, area blackouts are often triggered by an event that then causes cascading failures through the distribution system.
Your phone either works or does not (or is very noisy, but works). The electricity system has to handle anything from a tiny load to a city full of simultaneous cooking and air conditioning. What might be acceptable load in normal times could be overload if everyone fires up a big load at once. The electrical system is more vulnerable.
(Jerry Pournelle about 15 years ago described an incident where someone a few blocks away hit a power pole; this caused a 6000V line to drop onto the regular 220V distribution line, causing light bulbs to explode, electronics to fry, and general appliance failure for several blocks around. He was impressed that the UPS units protected some of his computer equipment from this “event”.)