It would create a duty finder matching nightmare. Causing queue's to be longer than they already are. A feature like this would cut down on the pool size people can play with and it wouldn't just effect you but the 3 (if doing 4 man content), or 7 (if doing 8 man content), or 23 (if doing CT) other people the duty finder system is trying to build a party with.
Lets look at a 8 man party.
2 tank, 2 healers, and 4 dps.
Duty finder finds all the people to create the party. And you (dps) have one of the tanks blacklisted. Well, I guess duty finder has to drop you from the party because the 6 other people (not including the person who you have blacklisted), don't have the tank blacklisted. Which means you are the weakest link on duty finder doing it's job of creating a full party. So, you go back to the queue waiting for a new party to be formed and the 7 other people just wait until another dps comes available. Their queue time would be must smaller than yours. What it would do it cause you to be pushed out of parties constantly.
Sounds annoying doesn't it? Now just imagine that a much larger scale where you have people blacklisting other people. Luckily you can only blacklist from your own server. The idea of blacklist in FFXIV is to essentially mute that person. It doesn't mean they disappear from the world.