AVL tree balance property states for the two subtrees of a node, their height can differ at most one. Why can't it be zero?
What matters is that the height  of the tree is limited by $O(\log n)$. As long as you maintain that property your searches will remain efficient.

Forcing the height difference to be zero we get the above property. However we also get the property if we allow the difference to be 1. The crux is that the latter requires a lot less rebalancing to achieve. The average height of a node will very slightly increase due to our more relaxed tree structure but this downside is greatly overshadowed by the reduction in rebalancing operations.