The most significant difficulty I see you run into is with the healer. As long as healing abilities are class restricted, you're going to run into class-role linkage. You can't be in a healer role if you got no healer powers.
Well one of the few changes made with 4E that I ultimately found favor with regards healing. I utterly despise their terminology of "surges" (and strictly
healing surges at that) but I think it is possible to better implement that basic concept.
Mostly it hinges on the idea across all edtions that hit points don't represent only physical damage. It can be fatigue, skill, protection of deities, and any number of other things. HEALING implies repair of physical damage but I see no reason why fighters can't rapidly recover
fatigue, why clerics can't grant "the favors of X", magic users convert mana to healing, monks ignoring pain, paladins of course lay on hands, and then everyone can still use potions, salves, Elven waybread, mom's special soup, or the processed sap of the wallawalla tree, etc.
If you spread the ability to RECOVER hitpoints through a variety of means over all the classes instead of saddling one or two classes with
exclusive healing ability then you have taken huge steps towards freeing the "healer" class to do something vastly more interesting and dynamic. The expected "support" class can be more than just a hit point battery or buff-bot. Those are deplorably narrow concepts of what can be done. It is quite possible for a support character to lend support by working IN CONJUNCTION with other classes or improving what they do through
active participation rather than passively providing buffs and then standing around watching the others do the
doing.
Then, anyone you want to actually label as a "healer" can be given much more interesting curative abilities to prevent or alleviate special conditions or types of damage.