When playing a healer, there's no single "right" way to play. Tanks can adjust their gear and strategy to boost their threat or avoidance, but both of those statistics are easy to track and monitor. Damage classes are obviously optimizing for one thing: DPS. Healers, on the other hand, can both get to the same point while taking completely different paths. Checking your healing per second on a healing meter won't show all of the times that you saved someone's life or made a great decision, and it never tells the whole story of an encounter. The best example is how your total healing done will plummet as your raid group gets better and better at avoiding damage on a particular encounter.
Healing meters do have a few useful purposes. They allow us to empirically test different strategies and gear choices, and we can monitor the effect of changes that we make. They also allow us to evaluate talents and individual abilities, which means we can make educated decisions about our talent and spell selection. When reviewing my healing done, I can figure out exactly what works and what doesn't. One thing has consistently stood out as negligible to my overall healing: Illuminated Healing. How did our mastery bonus end up so impotent?