According to Theravadin Buddhism, enlightenment is defined as freedom from greed, hatred and ignorance, a mind purified from all greed, hatred and ignorance.
Should it be our goal? It would be nice to be able to purify the mind from all greed, hatred and ignorance, right? And as we do this moment-to-moment, we are coming closer to the true purity of mind. If we want to be free of all Dukkha, then that is a nice goal for us all.