Just because it is 12V doesn't restrict it to one battery. You can link many 12V batteries, in parallel, to increase the Ah (storage) without changing the voltage.
The reason smaller inverters use 12V is cost (you only need one battery to start with, rather than a minimum of 2 for a 24V or 4 for a 48V system) and versatility (you can use it when camping and not have to have a 24V system in your car).
The other reason is the low draw on the battery. With a draw of 600W from a 12V/100Ah with 50% DoD you will get about 1 hour of usage (disregarding the efficiency of the inverter).
Edit:
600w with 100aH/12V battery will give 2 hours
You must never let the battery discharge below 50%, so that gives 1 hour
Modified sine wave inverters (typically used in smaller inverters) are only 75-85% efficient. At 80% you now have 48 minutes.
You generally don't use more than half the inverter rating so 300W will last you 1 hour and 36 minutes.
Your TV, media box / decoder and a few lights will quite comfortably run for over 2 hours.
If you plan to run at the full 600w then you need to add a second and even a third battery to be able to make it through load shedding. 3x100aH/12V, 600W, 50% DoD and 80% efficiency = 2 hours and 24 minutes.
The only other problem is small inverter systems have small battery chargers. So your batteries will take a long time to charge.