Unless you subscribe to their business plan and IP phone service, Cox would have nothing to do with a residential IP phone. It's easy to setup; however, on a residential plan, your QoS may suffer. For example, if you occasionally...or frequently...suffer Internet latency or congestion, your voice service would be poor. Business plans normally have more bandwidth and redundancy than a residential plan. I'm not implying IP phones and residential plans don't mix, but you'll need to be vigilant of your bandwidth.
It's easy to setup because after buying an IP phone, you only need to subscribe to a VoIP phone service-provider. The provider creates your account, assigns a telephone number and routes your packets. The provider may also register you for 911. "Oh, you live in Bismark, ND? We'll route 911 to the Bismark 911 Center."
Your softphone example is basically the same as Google Voice. Google sets up and maintains the call and sends voice packets to your PC. If you receive a Google call on your landline, the caller ID displays San Francisco...not the location of your PC.