Deep Cycle Batteries
the logic is correct but in reality it’s not that simple. Using the 225ah example, it’s easy to find a 225 ah 6v battery and they are small, light, and cheap enough to work with. A 225 ah 12v battery, if you could find one, would be more expensive, bigger, and heavier.
Another reason why the 6v batteries are popular is they have a greater capacity to be more deeply discharged and then recover. I believe this is due to the size and thickness of thier lead plates.
All of the above is just what I have found while researching this and hearing from other people, I am not an expert.
If you can find a 12v battery set up that gives you more amp hours for less money then that’s great. In my opinion, the 6v batteries give you more bang for your buck.