The way the Cox (and other cable company) boxes work is that they have an application running on their servers which transmits any calling numbers over the cable network. Each of those implementations are proprietary.
To have "universal" caller id your TiVos would need a phone jack (which they no longer ship with as of Series 4) and then you'd need to connect your TiVo to your MTA (the box from Cox) or your landline. Given the trend of no longer having a landline, especially I suspect among the type of people who buy retail TiVos, I'm sure this isn't a priority.
Current: TiVo HD w/lifetime, 2 x 2 Tuner Premieres
Former: S1, S2 TiVos, UltimateTV, SD DirecTiVo (x3), SA 8300HD w/Passport Echo, DirecTV HR-24 (x2) , DISH 722k, DirecTV Genie + 2 mini