It's a nice foundation, but the system lacks sources of conflict and hardships.
In your elf example, there aren't clear conflicts within the elven society. There is some potential for conflict against the elven society, if there is a nearby culture that will want to defile nature somehow.
If someone is using the system without paying attention, he could set the foundation for many cultures that will fit as background elements and not much more.

Ways to counter this while keeping the system:
1) Before and while filling the 3X3X3, thinking about what is the culture's role in the setting.
2) Filling some of it with things that are extreme, or that will be considered extreme by other cultures. A rule of "always try to free slaves" could be the source of many wars.
3) Making sure that there will be some sort of clash of values or inner contradiction. A culture that will give harsh punishments for crimes and consider compassion as the highest virtue will likely result in a lot of arguments and many vigilantes that try to save people from the law.
4) Put things that are inherently self-destructive. Values like "always fight to the death", "never hoard any resource, spend everything immediately", "we must always prove our superiority above other cultures".