If having faith means to be free of all experiences of doubt, fear, anger, or anxiety, then clearly those who wrote the Psalms were not people of faith. Genuine, authentic faith is the willingness to hold on to God in those struggles, refusing to let go even in our wrestling.
No matter how loud the voices of hurt, brokenness, and sorrow may scream, they are never the last word. Christ is always the first and the last Word, and He is a word of hope and resurrection.
We cannot neglect the corporate gathering of worship and still claim a biblical Christianity. We are never simply an individual following Christ; we are always part of the body of Christ.