I started this request for Duty Finder only on my server, in the feedback forums, so far the answer I got is that Yoshi-P said the queues would be too long. I kind of disagree, since I think if I knew there were people on my server who needed a dungeon for a quest, I would go help out - but if they are random people from other servers I won't bother helping. Perhaps FFXI players are more mature and helpful, we definitely had a reputation from that in FFXI and yes this isn't FFXI but there are still a lot of us, and hopefully we can set a good example for this generation of players.
I would assume you'd try to search on your server first, but failing that you'd go cross server, since it is an option - so eventually you'd offer yourself up as a player in the full cross-server pool. And others who care less about making friends/community would go straight to cross-server.
I made a post on the beta forums: http://forum.square-enix.com/ARR-Test/threads/106777-Option-to-link-with-only-players-on-the-same-server
And here too: http://ffxiv.zam.com/forum.html?forum=152&mid=137694411273901685&p=1#6
Edited, Aug 19th 2013 5:40pm by SyniteonReflux