Great question!
12V is needed because you don't want to run the HV battery and conversion system all the time, the vehicle has 24/7/365 12V loads so if they were going to run it off the HV they'd be running it all the time and that is bad for a few reasons:
1. the conversion efficiency isn't going to be great at low loads, this means you are wasting energy to the losses constantly.
2. if a vehicle is parked with a low battery and left for a long time (this happens sometimes) the HV battery is the last thing you want to sacrifice so you want another battery there to carry the burden of the 12V loads so that battery can just rest and wait to be recharged.
Tesla actually built the first 100 or so Roadsters under that same assumption that they didn't need a 12V battery, it failed them, they had a few bricked Roadster packs and quickly realized that wasn't the way to go. Any time an EV company tells me they are thinking of doing it the HV to 12V way, I advise them strongly against it!
OK, your second question; small 3 cell li-ion instead... Well that is a nice theory but doesn't work too well unless you design it right, and mostly auto manufacturers (even tesla) don't have a lot of experience with 12V battery designs, it is quite different than high voltage, and to be honest a low-level concern for a big company like TESLA. This is where start-ups like
www.ohmmu.com (shameless plug for myself here) come in, we know how to design these batteries to work in the specific vehicles they are going to go into.
To further answer this second question with what is perhaps the biggest issue from an OEM stand-point; TEMPERATURE! as extreme cold charging of lithium batteries leads to plating and ruins the battery, to avoid this certain things can be done in the design. This is a big part of what I'm doing with my Ohmmu company, we are working on ways to improve this extreme cold weather performance. Most auto manufacturers follow an "automotive standard" 12V battery operating temperature range; this range is -40C to +85C (-40F to 185F). For any off-the-shelf lithium battery solution that range is untenable, impossible to guarantee. As we work forward with our technologies and strategies we hope to get to the point where we can provide the exact same range in our spec! At this time, we are getting closer and closer, while the reality is that for a tesla the 12V battery never hits those extreme temperatures and so they really don't "need" to spec their 12V that way, but its a standard thing so they do it...
I will tell you, without specifics, we (Ohmmu) are presently working with OEM's to deploy lithium 12V systems as OEM in the future! It's a very exciting thing and I am very passionate about it and believe we will get there!
Sorry to be so long-winded here!