If you want X to buff Y and X goes before Y then problem solved. If you want X to buff Y and Y goes before X then Y saves AP and X buffs immediately, giving Y extra AP on their turn with the buffs.
No one said you had to skip both of them.
It's not often that simple.
Most of the time, it's X Y Z (I have 1 Lone Wolf). Like Gyson above, I have a Ranger; sometimes she'll get the Oath of Desecration, sometimes the warrior. If it's the warrior and he's getting 2-3 buffs, delay simplifies that process, and he can act again at the end,
all statuses intact (as in, warrior was X; waits, gets buffed by Y and Z; acts with all buffs).
Why is this significant? If warrior X WAITED and gets buffed by Y and Z, next round, his buffs are already depleted by a round. By delaying, he's made full use of all his enchantments (once at end of round 1, again beginning round 2). Oath of Desecration lasts 3 rounds; if player A can only attack once a round, by delaying, he puts out 3 attacks for the duration of the spell. By waiting, he puts out 2 attacks while under the buff.
Or as Gyson mentions as well, the star use of delaying for me is also setting up other character's attacks. I also have bully, and a double turn often means death for at least a few foes.
So maybe in summary, delay gives us flexibility. If I wanted to buff Jahan (he can only take about 2 hits), that's doable too, and I wouldn't want him to save AP, because Glass Cannon would waste some next turn.