Cox doesn't block all ports, and they do provide a list of the ports they do block and their reasons for blocking them. Of course anyone can see through their reasons, but none the less, there you have it.
You shouldn't be having problems porting to your games. If you are, then you need to double and triple check your settings, ip addresses etc.
As far as home connections go, mine is very complex and secure, with three separate networks on the 192, 172 and 10 ip blocks, and I have plenty of ports open and forwarded to the various networks. I've been doing this for 30+ years on commercial service. This includes ports for games, ssh, sftp, plex, remote login to numerous computers, applications etc.
I'm not defending cox, believe me, I've had my run arounds with cox's so called 'tech support'.