With the proliferation of cell phone internet and hotspots you'd have to take down the cell towers along with the fiber lines and TV cable services. It's easier just to kill the power to the city. You'd still have satellite internet but how many people actually have that access inside a city? Even if someone did have it, they'd have a hard time powering the transmitter/receiver without the grid operating.

In addition to taking out the internet, you also take out air conditioning, hot water, microwaves, fridges and other 'everyday wonders' everyone takes for granted. Sure you'll still have a few 'off grid' power sources but inside a city those would be extremely rare to the point of being inconsequential.

Hospitals are required to have backup generators and a weeks worth of fuel so you wouldn't be endangering them and water/sewage has their own backup power supplies in most cases.

The goal wouldn't to be to kill the city but choke it into submission if it was put under siege.

Please note that I'm not advocating for anyone to do this but to get into people's heads that living in a big city is actually a trap if it came to open conflict.