Pretty hot topic, ya? It's pretty easy to see the division between players who have used parser and those who haven't and don't like the idea. I think it would be fair to say casual players fit into the latter portion. And considering that this game was built to be casual friendly, I think I understand why SE doesn't want it in FFXIV. To be fair, parser can be very helpful for more hardcore players doing top tier content. Being able to see the numbers of an encounter can pin point the any issues, save time and gives a greater understanding of what the problem is and then being able to solve it quicker and more efficiently. Now, having said that, the other side of that argument is that parser can be used as a tool to judge a player based on a number crunch alone. And more importantly, it would bring a divide between the players on this game. You can read this thread and see how divisive parser can be. If parser was to be implemented, I could see the casual group becoming more hesitant to use Duty Finder because they know other players are judging them even more, and having the raw numbers to tells someone they're not doing their job right or that they're a bad player can be really discouraging. Especially for people who play this game just to relax after work or on the weekends.
I've played this game without a parser since 2010 and FF11 before that. I have also played WOW for a good bit and I have to honestly say that without a parser there is less drama and fighting. But on that same note, when I played with a parser on WOW, I noticed players were quicker with their damage, and instances were almost like a rush to see who could do the best damage making everything much faster. It shines under the right usage, but can be abused as well to ridicule, troll and belittle other players who aren't as experienced. We see enough of that as it is, ya? SE knows the problems it causes. It has its pros and cons but they decided against it.