Why are stable ionic charges so strongly related to the group number?

Why do lighter elements have ionic charges so strongly related to the group number? For example, why does $\ce{Al}$ only show +3 ionic charge? The basic concept of stability in an ionic compound is that lattice energy is greater than the sum of ionisation energy and electron gain enthalpy. Why can't $\ce{Al}$ show +1 or +2 states? I understand that the +3 state is in a 'sweet spot' since going from +3 to +4 requires a large amount of energy whereas going from +2 to +3 doesn't require much. Besides, a higher charge results in more lattice energy. Hence, it makes sense that the element would want to have the highest charge possible. This explains the abundance of ions in those states but not the absence of others. Why is it that the energy calculations always work out for lighter elements so that they only have the highest charge possible? Is it just chance or am I missing some deeper principle here?


