Like you guys said about parsing, the HPS numbers just don't seem to carry much weight, but still get thrown around as equivalent measures like DPS.
It's important to note that a healer's ability to burst hps when it's needed is important.
As is the approximate maximum hps a healer can sustain for the duration of a fight without oom'ing.
... does the amount you end up healing on a given fight show either of those things? NOPE, not unless the person evaluating you goes to a WoL *parse* to look at what you healed moment by moment... and even then, the parse may not show your actual capability if the raid is overhealing the fight (overhealing in this context = too many healers present for the amount of damage actually being taken by the raid).
... lots and *lots* of guilds overheal fights (mine being one of them). Usually, dps requirements are low enough that in 10man, you can bring 3 healers instead of 2, and having that 3rd healer (and importantly, the 3rd set of healer spec cooldowns) means you can heal through the derp of the raid in numbers of situations, instead of wiping. It generally gives people more leeway to make mistakes.
However, this means that large numbers of 10man healers are "competing" for a limited amount of healing needed to be done, if you look at "who does more healing" on the meters. The same happens in 25man too, but I'm not on top of how many healers it takes to overheal 25man content.
Now, if during a clutch mechanic, you *can't* burst as high as the other healers, then that can be a problem in fights were x amount of burst healing is needed, and you need to learn how to adjust your gear and potentially your glyphs/talents, as well as your playstyle, to get up to par for your class & ilvl, in that case. That's not what you're describing
, but it's one situation in which a healer's situation-specific hps (as measured by the burst shown on your graph of "healing done" on the fight) *can* be important.
Far more important than a healer's hps is all the other info WoL will give anyone who's looking at your parses in depth - which talents & glyphs you choose to use for a fight, when & how you use your cooldowns, your active mana management, and a general idea of what abilities you use to sustain however much hps is needed outside of burst requirements.
As everyone else has mentioned, it's unfortunate that so many RLs are clueless about how to identify a good healer. It holds their raids back, and discourages perfectly good healers who are told they're a problem for the raid.