Works Best. Cox certifies specific modems due to its underlying technology. Just because Cox certifies a modem, it doesn't mean it's any better than another brand. It just means it's compliant with the Cox configuration. I'm sure there's a "world's best" modem somewhere but if it doesn't comply, Cox can't certify it.
Tech Support. Cox issues a list of certified modems so you can either buy it on the market or from Cox. Either way, it's the exact same modem. If you did purchase from Cox, there would be no additional tech support for the modem.
Puma-6. You could have just as easily purchased the faulty chipset from Cox. If it was within a Cox-rented router, however, I'm sure Cox would have replaced it but it'd depend on the firmware. I can't remember...what did Cox do with rented Puma-6 equipment?
A router has nothing to do with a Cox configuration. A router is your network. If you want the ax router...stop renting and buy the ax router.