These are certainly useful ways to increase our understanding of liturgy, but I would like to propose a more personal and visceral account of the liturgy. This may seem an odd starting point, but I think that Zen Master Dogen had basically the right idea about the purpose of liturgy.
"In ceremony there are forms and there are sounds, there is understanding and there is believing. In liturgy there is only intimacy."
The fundamental purpose of liturgy is the same whether we are Christians of the ancient Church or Zen Buddhists: the liturgy exists to bring us into an ever deepening intimacy, and in the case of Christianity this intimacy is in relationship with Christ. The other ways of viewing liturgy lead us to this same point. In looking at the origin of the term we learn that the liturgy was indeed a service to the people to reconcile them with God and was indeed very costly, a cost paid by Christ's sacrifice on the cross. In looking at the variety of rites within the ancient Church, we learn that there are many ways to cultivate that intimacy in the liturgy within disparate cultural contexts while maintaining the same underlying structure and theology. In looking at the rubrics, we learn that the underlying structure and theology are there to help keep us focused on our beloved Lord by providing the boundaries which draw our gaze and will to Christ, which assists in preventing some of our many distractions from creeping in and ruining the intimacy we seek.
"Haven't you heard the ancient master's teaching: Seeing forms with the whole body-and-mind, hearing sounds with the whole body-and-mind one understands them intimately. Intimate understanding is not like ordinary understanding."
While the Zen Master's words might seem otherworldly to Western readers, the experience of intimacy is one that many humans understand at least to some degree. We have experiences of intimacy with family, longtime friends, and spouses. We all know that our relationships with those who are intimates are qualitatively and quantitatively different from our other relationships. Intimate understanding between persons makes conversation less necessary because we already have a strong sense of what the other is thinking or feeling. It generates an abiding joy which can weather the many difficulties of human relationships because we know that this relationship is deeper and more important than the petty daily squabbles or even the lifelong ailments.
Intimate relationships are cultivated by creating a special place in one's life for another person. Our intimate friends get more of our time, our experiences, and our burdens than others. They know us more deeply, and we often have special ways of greeting and communicating with our intimate friends and family and spouses which do not apply to other relationships. In the same way, we cultivate an intimate relationship with Christ by spending more of our time with Him in the divine liturgy, by sharing our experiences and burdens with Him in prayer, and by greeting and communicating with Him in a way that conveys that he is our intimate friend and deeply important to us. This helps us to build the profoundly loving relationship we so desire to have with Christ.
In healthy intimate relationships, we tend to take on the good qualities of those whom we love, and this is also true of our relationship with Christ. The more time and effort we put into building our relationship with Him, the more we begin to become like him in all His virtues. In the same way that holy Christian friendships and marriages help us to smooth out our rough edges and become more Christ-like in mutual service to one another by learning to value those relationships over our selfishness, so to do we starve our desire for anything that would hinder our relationship with Christ by serving Him as he pours out His grace upon us.
In the liturgy, we lift up our hearts in love and are lifted up in the embrace of divine love, and by this love we gradually put to death those parts of us that can not partake of divine love.