Chiang's story was an exploration of a more Eastern mode of thought in which purpose is derived more from participation. That we are all part of one large tapestry of life and that it is the privilege of participating, not the end outcome of the participation that gives purpose to life.
Louise is placed in a circumstance where these two values come into conflict and, crucially, is given a choice. The crux is that she is given the choice to not have her child and prevent all of the painful memories but also the understanding that the painful memories are a part of the beauty of living life.
The variational physics stuff is all a frame to wrap around these concepts, finding resonance between the idea that there are always two ways of encoding a problem in physics and the reframing of philosophy that comes from encountering an alien culture.