If we talk about raids, tanks rarely die from a lack of sustained healer HPS. Its burst that kills tank. Haste does the most for that by giving you 100% ISB uptime and letting you purify off the High stagger from these burst windows.
Mastery reduces the chance of such a burst happening but only works against Auto attacks and not abilities which are often (always) more dangerous.
Crit heals your healers cope but does nothing to reduce the killing burst itself.
Now you ofcourse don't want to ignore Mastery/Crit because if they go low enough healers will indeed struggle, as with most things in the game some sort of balance has to be maintained.
For dungeons this changes because there is more pressure on the single healer which increases the value of Mastery/Crit.