"in the living room"
You've hit on one of my primary objections to mandating CO detectors: placement.
There's no settled doctrine as to the placement of CO detectors. The NFPA standard, after a lot of doubletalk, refers you back to the manufacturers' instructions. The instructions ... well, summarised simply, do not find a problem with any placement you might suggest.
Part of the problem lies in the nature of CO. It's not much different, in density or temperature, from the surrounding air. There is no compelling reasom to place it in any particular location.
The other problem lies in the way CO affects our bodies - and, by extension, the way detectors are designed to operate. The less CO that is present, the longer they take to to go into alarm. This is quite different from a smoke detector, which won't ever go into alarm until a specific level is reached. It's also why having a CO detector with a readable display is a good idea, and why there is such an advantage to the corded units. Just like with the "Valentine One" radar detector ads say: there's no way for a battery unit to perform as well as a corded unit.
Getting back to 'the problem.' The sensing elements can be fooled. Instructions often illustrate placing one in the mechanicals closet, for example. The problem here is that the initial plume of CO or even hot air from an appliance igniting can create a false alarm. Likewise, gas fumes can set it off. So, that initial puff of gas before the igniter strikes, and the momentary flare of a poorly burning flame, can set off the detector - even though no hazard is present.
IMO, you don't want these alarms anywhere near the appliances.
As others have pointed out, we percieve sleep time as the time where we are most at risk from this 'silent killer.' With that in mind, I DON'T want the detector outside the sleeping area. Simply closing the door can create a situation where the air in one room differs from the air in the next. I want that alarm near my sleeping head - but that's my opinion, and IMO a design matter.
As far as the requirement ever being added to the NEC goes, I doubt that will ever happen. As with smoke alarms, you'll find these requirements in the 'other' codes. Copies of the IBC, IRC, IMC, etc., can be found at BulkResource.Org . You need to know more than just 'your' code.