I've had to tell countless friends and other people - Do not think of healers in PVP as healers. They're DPS with some support tools and CC. Do not give critical priority to killing them (Maybe to white mage sometimes, but it's because of its stun limit break and polymorph CC) - but really you should kill opportunistically. Still, a lot of people act like healer's are as important as they once were and throw matches focusing them at all costs, when really they should deal with that dragoon destroying the team.
The main thing in PVP, however, is to understand the tempo of the battles. Look for when people pop their big burst, and then know there's little they can do to hurt you for 10~15 seconds. Especially as you get to higher ranks, just diving into the middle of the enemy team is often an insta-death sentence. When you understand the tempo well enough to understand when you're about to get focused by a bunch of burst, you can pop guard to negate that and make them waste their abilities - or at least stall them.
As for the game as a whole, outside of pvp. Well, let me put it this way. The game certainly isn't going towards a direction of healing being more important. If the healer dies, or if you preform and just don't take a healer, it's no big deal for more and more content. Makes sense for PVP to move in this direction too, but PVE doesn't have the other spaces to expand into like PVP does.