Face Classification. Is it OK to only use geometric features?
What lies at the heart of pattern recognition and pattern classification is the selection of the correct features that is used in decisions. And the most important properties of correct features are 1-ease of measurement , 2-power of discrimination. So not every feature is the same. And finding the ones which yields the best performance requires research, creativity and expertise.

In your problem of face recognition, you should first find those features which most critically depend on particularity of the member of their class, but should also be easy to measure. Geometric features provide both powerful and easy to measure examples. Therefore you can rely on them. 

But depending on your aim, you may consider using other features as well, if you want a better discrimination of members. So therefore it depends on your requirements of discrimination fault tolerance.