That's the reason why you should try to boost initiative of your supporting chars. In a "perfect" party the supporting mage starts (in order to boost the melee's stats), followed by the melee to do great damage and at last the ranger/rogue and the second mage (for example) in order to stun/freeze enemies before it's their turn.
Example:
Supporting/boosting mage: 16-18 intitiative
Melee: 15-16 initiative
Others: 14-15 initiative
No real need for delays.

I play on hard, and at least for me, delaying is an essential part of my strategy. That way, my mage doesn't have to have the highest Initiative (Jahan doesn't), but can still buff my warrior, even if he were ahead in the turn order (but delayed). He'll get his full complement of buffs before he acts at the end of the current round.
Also, there seems to be little difference between just saving the AP and delaying, but IMO...I dunno, it feels better? Haha. Battles tend to start with enemies all over, but letting them go first, they often run towards my group and naturally clump. My Jahan has Glass Cannon, and if he just saved his AP, it'd be over his max (since recovery is doubled, but not starting).
I don't tend to delay if I'm confident enemies can shoot me or cast spells at me (to avoid CC). But if foes can't and they stray closer, my warrior (now buffed from lower Initiative characters) can usually Ram them, and get off another swing. And like everyone says, you tend to start first--it's like a double turn for my warrior. Very little survives a double smackdown from a heavy hitting melee character with Oath of Desecration, or if they do, I have another chance to CC them. I've found this essential for hard, as your party can't take that many hits.
I've found that since my party always has more initiative than all enemies, it's always better to simply save AP instead of delaying.
Not true.
You can lose AP by passing instead of delaying. Usually not the frist round, but certainly after. You also can manipulate action order for your characters. Heal before a DOT like burn goes off. Haste before your character attacks.
If you'll get so much AP you'll go over your max, then just spend some of it to help the position. The only time delaying is useful is if you aren't at the front of the turn line, which in my experience never even trying to get initiative is basically never.
I spend as little AP as possible to position--let them come to me is my philosophy.

tl;dr--when every AP counts, enemies do higher damage than normal, and you are squishier than normal--at least for my game, delaying is a cornerstone strategy.