This - exactly this.No one is responsible for your survival but you. And you will survive a lot longer is you have a way to heal up during a quest.
That said, there is a general understanding that clerics heal people. Especially during fights. You need to expect this and adapt to it in a way that works for you (and your party).
There is also a general opinon that FVS and to a lesser degree Brds are also healers.
That is not always the case, as they must specifically choose to have cure spells in their available spells.
All classes should strive to be "professional adventurers". Professionals do not need or beg from others. (most of the time). Some can not afford to be prepared for eveything. Some do not know how to be. And raging Barbarians have a special handycap in this area.
Plus the "hero" method is a good tactic, and a way of life in some raids now. It requires a dedicated healer.
prefessional adventures watch red and blue bars. They watch blue map dots. They see when others are in trouble and assist as best they can.
Sometimes that means healing. Sometimes it means trying to get agro off of the guy in trouble. I throw Displacements, and other buffs....as well as wand whip when I think it is needed to save somenone's life.
Preferably a group will act as a team. And players should at least try to play for the team even if there is no organised coordination.
All of this really means that clerics should heal others when they think they need it. With the goal of saving their life and assisting in getting the team ready for the next fight. As well as any other class that has the capability to do so.
(Talon, that was very well put. +1)
It does all boil down to teamwork.