It sounds like you don't know how these things work. Cox doesn't own the poles. The electric company does. Cox just leases the space. They can't even begin to work on a issue until the power is restored and any downed trees are removed and the roads are accessible. Also, HFC service is a lot more temperamental then electrical service. There are multiple amps and nodes that can be damaged or not have power. Just because you have power doesn't mean there is power where Cox equipment is. Some of that equipment has generators, but not all, and even the devices that do, the gas eventually runs out. It is NOT as easy as flipping a switch. That idea is absurd IMO.
Yes, the outage notification system needs to be improved. At least now they have a outage map. Before they didn't. They also added text notification. Many such system aren't very accurate because of the nature of the system. It's not just Cox though. I have Frontier and my entire state was affected by a issue and their outage map showed nothing. So if you don't like how Cox does something, try looking into a different ISP. Remember though, the grass is always greener on the other side.