Haste was a staple back in EQ, it was a requirement to have a bard to constantly play haste songs to help the party out. EQ also had/has a very different combat system than FFXIV, so it is irrelevant. (I just like EQ a lot, so I bring it up when I can.)

FFXIV does have a few hastes as others have pointed out, but they are not a constant buff, rather intermittent. The closest you get to a constant haste buff is the Astro's arrow. I you can constantly draw them and place them on the right job, it could be rather OP. But as the cards are RNG, and you will rarely ever get the same card more than 3 times in a row ... the haste becomes largely irrelevant in boss fights.