As a Holy Paladin leveling up, every kind of item is usable by me as long it has healer stats. However, I can only need on plate. That made me lose items with stats like mana-per-second to a feral druid.
Is it possible to let healers roll need on every kind of gear?
That sounds like a remarkably bad idea for the sake of the game, almost as remarkably bad of an idea it is to level up as a healer class, considering RDF content isn't truly insanely active (due to the x7 nature of the main two servers). Your suggestion would open a door for a lot of situations where an argument between a, say, balance druid and a holy paladin would occur, due to a leather item with spirit, or a mail item could create an argument with a shaman. Your best bet is to actually speak to your group, to whoever wins the item and ask them if they truly need it. Leveling is made so fast and a breeze to go through that itemization truly shouldn't necessarily matter, as you can dress yourself from quest rewards alone and still make it to max level.
As far as "healers get to roll on everything" on max level would go - that will end up DREADFUL!