I'm not power company person or electrician. This is observation of those in the demanding and dangerous trade of maintaining the power grid.
The power companies have a good triage system and it's time proven. Fix the biggest failures and work your way down the list till you have only the few that have had the wires ripped off the house and need an electrician. Its and exponential decay to near zero. The last 1000 will take much more time to get fixed than the first 100,000. I've been watching them and they are tired and have been hustling. Still its about equipment and bodies as often a few people are needed to handle some problems and other require whole crews and specialized gear. It's fairly amazing that the industry has evolved that guys from Wisconsin, Vermont and the like can roll in with trucks and bodies and go to work effectively and safely.
The actual damage repair is interesting. They find a break or blown interrupter and the first thing they do is follow the line for other damage. The initial information comes from police looking for downed wires or poles and other trained eyes as well as phone reports of outages. If the damage is a side road they will break the link to that and then keep searching. If they have cleared all the faults they go back and power up the section and work their way down the line to the shut off sections. Sometimes like our area they have to power the section down to work on the fault before they can bring it all up safely. In our case the top line is 7.8KV and hacking tree limbs near that is very unsafe. To do that the lineman has to go to the source point and open the interrupters (fuses or pole mounted switch) and safe the line by installing a big fat jumper to ground in case someone else powers it due to improperly installed generator, other line faults or some lineman coming down to help and closing the switch. Once the line is safe the fault can be dealt with in our case a tree limb on the wire acting like a short circuit. Once that mess was cleared the lineman has to move back the cutoff point, remove the safety and restore (close) the interrupter. If all goes well the lights work. Repeat until relieved or too tired to be safe.
That said I'm watching Katy's kid, TS Katia now. I'm not putting the generator, cables, aux power sources, or other tools and gear away just yet! I will refill the gas can.
Be prepared, prepare before the first hint of trouble, and keep your power dry.