Ofc the trick is doing max DPS while healing, we all know that you don't loose DPS to heal properly, and that a good healer should do max DPS while healing too.
Healbot in this game mostly doesn't exist as a role.
And ofc your sentence about DPS is true (we all know that most 6men are DPS races bla bla bla).
Still if you join random pugs with non experienced people ("training runs" as Misiuggah described them) and not well geared tanks, the extra
Heal Rating especially from Bears will impact the group more than the extra DPS you can get with Tiger's chest over Yag chest.
Instead, if your tanks don't need Heal Rating and AA heals to survive ofc an Heal Rating set is a waste and just impact the group in a negative way, for the reason you said.
But there are reasons to get that blunt imho...
After it got changed, if I should just choose a single blunt between that and T2 for 6men I'd just choose that: Constitution is not needed for most of 6 men, extra Hit Rating is nice and DPS is not too lower compared to T2 blunt, and the high Heal Rating is a nice addiction for Celestial Gaze (even if not using bears).