It would be great if the game rewarded both tanks and healers more for JUST doing their job and nothing more. Unfortunately, the way the game allows most skill expression is through damage, and for tanks, it is juggling their damage and their tank stances.
There is a point where tanks and healers learn that they can do more than just hold enmity or heal damage. That is where they learn that they can speed up dungeon runs or fights or pass a DPS check in high-end content. And it doesn't take that much effort to switch to a damage stance or cast a damage spell. Unfortunately, I believe healers are the most culpable at times because of the way the game is structured and the expectations players unfamiliar with how enemy damage operates.
Case in point, would you be okay with a healer who does nothing but cast Medica/Helios/Succor every once in a while and then stands there doing nothing? With a tank, it's less obvious that they are not putting in damage numbers, but when you see a healer stand there for up to a whole minute until the next raidwide or the next tankbuster, would that sit well with you? In most cases, if both healers in an 8-man duty were to DPS when possible (whilst still doing their healer duties obviously), they would almost always add up to another DPS's worth of damage. Considering that there would always be a couple of people who make mistakes (because we're all people after all) and therefore lower the party DPS, wouldn't it make sense to have everyone - including healers and tanks - add as much damage as they can whilst fulfilling their roles? Is it fair to a DPS player who has to press buttons every half a second to witness a healer player simply press a button every 30 seconds? Of course not.
Parses show you who is doing the least damage so you know which person is best to buff. Parses can tell you who is familiar with fight mechanics and who needs a pre-emptive heal in case they fail mechanics. Most of all, parses can tell who is putting little effort by class based on swing count. Never in my time of playing FFXIV have I kicked anyone for a low damage parse. I am sure other people have at some point, but to me, parses are simply there to tell me how I can adjust to other players.