Vyvyan Basterd
Adventurer
1) And one big effect that Perform (Haiku) had in 3e if I was a fighter was that I could roll to see how well I did, and have a "mortal baseline" to compare it against.
2) I could challenge wandering minstrels to Haiku contests in exchange for precious information.
3) I could roll well and deliver a well-crafted Haiku in the presence of the suspicious baron who thinks that all adventurers are trashy vagabonds who make a mess.
4) And if I multiclassed into Bard, I could use it for my Bardic Music.
5) And if it was a big part of my character, maybe my DM and I could synch up on some Haikunomancer PrC that helped me multiclass Bard and Fighter without being too gimped.
6) I could gain (and quest for!) several Perform or Cha-enhancing magic items, many of which I could use with much more skill than any other fighter.
7) But perhaps the most significant thing I could do with Perform (Haiku) in 3e that I can't do out-of-the-box in 4e is actually have and use a Perform (Haiku) skill.
8) 3e's system might not have been amazing, but, compared to 4e's system, it gets the job done better.
1) I would inform you as a player in my game that your ability to perform haikus is covered as a Cha check. If you wrote a solid background that incorporated the use of haikus in an interesting way I would give you anywhere between a +2 to +5 bonus depending on their imporatance in your background. I couldn't have done this in 3E without you having to devote one of your two skill points to Perform (haiku) or you would have never improved in your haiku-spouting.
2) Goal: Gather information. You would use an appropriate skill to gather the information. By tying the skill into an important piece of your background under appropriate circumstances I would give you a +2 bonus to your roll.
3) Goal: Diplomacy (or Bluff if you really are trashy vagabonds). Again with a possible +2.
4) I specified Fighter, not Bard.
5) You could co-develop a Paragon Path and/or Epic Destiny based on haikus with me.
6) Most published 3E magic items that required perform skills required a specific one. I feel safe saying that Perform (haiku) was not a requirement of any published one. So, you and your DM would have to develop one. We could do the same in 4E.
7) See #1.
8) We obviously disagree.

Now to answer my own question:
I would have my fighter spout haikus in battle to try to demoralize enemies. I'd want my enemies to wonder who this wacko is spouting ominous poetry in the midst of warfare.
Goal: Initimidation. I'd tie my haikus into my skill to initmidate.