Mostly because it was designed that way. But each has a different peak operating range: 12V - the common car systems such as lights and control computers work on 12V mostly because ordinary car accessories are designed for 12V. 200-270 V traction battery - has to send and recieve significant electrical energy. It is not uncommon to see 50A @270 V on my older Prius, this is 13,500 watts. If it were a 12V battery it would need over 1,000 A. and the conductors would look like pipes ... big pipes. Worse, the "I squared R" loss increase by the square of the current and we would lose a great deal of energy. If I remember correctly, the SAE paper on the Prius c shows the traction battery-to-12V converter is part of the battery assembly. Someday we may see the 12V battery go away saving about 30 lbs. Bob Wilson
In addition to the above, it appears the early hybrids use the 12V as a safety mechanism. The ignition key and safety checks and I guess running the radio and interior lights are like a normal car and everything depends on the 12V battery. The high voltage stuff is all disconnected physically and there is no danger anywhere except inside the battery case, until the key is put to ON/READY where the car computer checks things and decides if it is safe to enable to contactors (large physical relays) to connect to the high voltage. So, they could have maybe implemented this with a single rechargeable cell and done away with heavy lead acid, but all the ECUs and car components have decades of design and reliability around a robust 12V lead acid.
In other words why can't the hybrid battery handle all the mundane tasks? I'm not sure, maybe due to different voltage; it's too expensive or involved to step it down to 12 volt?
Once you are in ON or READY, the HV does handle everything. You don't have an "alternator" but the DC-DC is always putting 13.5 to 13.9V on the 12V battery. The 12V battery is used in ACC and when you "start" the car. It is why you get bad mileage with an old 12V battery.. the first 10 mins of driving, the ICE is charging up the 12V battery with current. (Or more accurately, the ICE sending current through MG1 to the HV battery and inverters and the inverters/DC-DC is sending current to the 12V battery). When the car is off, the 12V battery is the only voltage in the car and handles the keyless entry, the windows, the interior lights, the radio, etc. The HV battery is disconnected to the world until you put the car to ON.
Vic, At some point, would you ask your "relatives" where they are getting all their information. I think it is great that you are making the efforts to learn about the car and are willing to make the effort to educate your relatives, but at some point, you should inquire about their sources. Sources like "it's common knowledge" or "everyone knows" are indications that they are just spreading manure. I had to do some explaining to my mother when I got my car (right after dear Mr. Sykes had his "runaway" incident in San Diego) after 3 or 4 questions, she realized I knew my car and my research on the car and just opted to worry about me rather than worry about me AND talk me into another car. The 12volt battery will cost ~150 to $200 to replace. I had to replace mine early (< 2 years) likely because it had been abused (drained) at the dealership before I got it. I have high hopes for my replacement Optima.
Another reason for a 12V battery is that the HV battery would be seeing much much more discharge usage of it's lifecycle if you had an always on 12V DC-DC running. So if you left it for three days, the HV battery would be losing 10% SOC or something (probably way less) running the keyless entry and also running an inefficient DC-DC converter and tons of milliamps to run an ECU to monitor the HV battery. By using a 12V lead acid, that can safely discharge for days running the keyless entry. No worries if you left a light on, you are only draining the 12V. And the 12V gets recharged from your ICE through wasted MPG. You "could" do the same thing with the HV battery, but then you are giving up some percentage of the lifespan because it would be losing 10% over a week and then it would have to charge back up 10%. Also the 12V disconnect means the HV battery is complete disconnected, and if anything happened when driving, you still have a 12V battery to run things if the HV shutdown. (Though they also included a huge capacitor bank for the brakes in that situation).