Warlock Lord,
It seems you assume the characters, and everyone else, knows what class they are. So a character trains in the army; he doesn't think, "I'll take a level of Fighter", he thinks, "I want to get better at fighting". Similarly, a character classed as a Sorcerer can be an ordained priest, though he can't heal or turn undead; a bard may pass himself off as a powerful Wizard, and who would gainsay them?
Class levels, PrCs, HD, etc are metagame knowledge, and thus completely unknown to the character, or anyone immersed in the story of the action.
You say "All wizards can heal", but as the reader of these stories we are only privy to in-game knowledge. We don't know if Gandalf is a Wizard, Druid, or Cleric. We don't know if the Grey Mouser is a Fighter/Rogue, or a Bard, or a Rogue/Wizard. Even if they use a specific term like, "Sorcerer", we can fairly easily say that the term is not a game-term but an in-game appellation.
The Point: don't equate literary terms with game terms.
In every fantasy story, the wizards/sorcerors/arcanists of the land can heal injuries.
Hyperbole.
A character classed with levels of Cleric can call himself a wizard.
A character classed with levels of Druid can call herself a witch.
A character classed with levels of Bard can call himself a sorcerer.
You now have literary precident for wizards, witches, and sorcerers healing people, even though it has nothing to do with their class levels.
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Is it essential that a class be able to heal? Yes.
Are the arcanist classes powerful as-is? Yes.
Would granting arcanist classes healing ability make them more powerful? Yes.
Would seperating the healing ability from arcanists make them less powerful? Yes.
Get the drift?
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By the by, it seems ironic that you seemingly condemn classes as "Sacred Cows" that exist merely by virtue of having existed in the past, and then go on to cite past precident which you think should be followed... which if it were, could very easily be ridiculed as a "Sacred Cow". Why? Because it's merely a continuation of what happened in the past. Hmmm.