Against the different boss, heavy healing is necessary. Starting with the third or so boss, he will hit twice per round, often with multiple target spells (megastorm or something like that in english, for example), so heavy healing is needed. Plus, some can heal themselves, drawing the battle in length. A dedicated healer is, in my humble opinion, necessary. Even with a priest dedicated to healing, I am sometimes constrained to use the healing spells of the main character to keep the whole group alive.
Unless you manage to have a damage output of hundreds of damage per round, you won't be able to kill a boss before he kills you.
Edit : Sometimes use of buffs/debuffs is mandatory. You won't survive a heavy hit with an alteration on your party and you won't damage a boss with protection on him, thus, you must counter those spell with the appropriate buffs/debuffs, and a buffing/debuffing player does not deal damages. Likewise, you have to counter alterations effects (sleep, paralyze, etc.). Also, the time a member of your party is healing himself or another one, he doesn't do damages. Having completed DQ4 and 5, and seeing DQ9 is the same and even harder, I can tell you cannot survive without proper healing.
The healer is quite useless on random monsters encountered on the map. My personal advice : specialize your healer in magic wands, this way you can regen the MP of your healer on the random encounters to arrive fully charged against the boss.
A big reason to try out different vocations is to farm skill points.
For example, if you have a character who is a priest and you want him/her to learn wands. You could spend points you get from leveling up as a priest on your wand skill, but then it would be tougher to level up your priest vocation skill.
Instead you could make your character a mage, point all those points you get into wands, then switch back to priest. Then you could use all your priest points on your vocation.
A second reason is because maxing out an equipment skill at 100 points lets you use that skill on any class, even if they don't have it available. Martial artists for example cannot use shields, but you could level your martial artist as a class that can, get shields up to 100, then when you switch back to martial artist you will be able to use shields.
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Other than going back to the Inn at Stornway, I haven't seen a way of doing it. Just one of many little things that drives me nuts about this game.