See you don't rent the box in most cases, its the "Programming Access Fee" or some other similar term. So they would still charge the $7-ish every provider charges.
You can buy your own system compatible box and they still charge full boat.
Totally different purpose. Cable card is an authorizing/permission device only. and HDMI is an input port standard. even if your TiVo has HDMI it also need the cablecard to get permission/instruction to decode ONLY those channels you pay for. Cable card one was a clumsy standard force on the CATV industry. while cable card 2 received marginal hardware support due to the failure of CC1. The actual CATV and hardware industry have tried offering several different solutions, cheap to embed in every device...potentially a real, usable standard only to see it pushed away by one of the four table legs (regulators, content owners, hardware suppliers, CATV providers) each afraid of losing control over their own segment. Until you find something all for can support that is cheap enough and transparent enough for the least technical consumer, you will be stuck with the overpriced and extremely limited Cablecard standard.