Klepsacovic explains the advantage of cross-server dungeons, which is mainly a significant decrease in queue time. Outside prime time that cross-server function makes all the difference, enabling you to actually find a group before you play session is over. Of course Klepsacovic is right in saying that this might be less needed during prime time. But I'm not convinced yet that the cross-server functionality actually has any disadvantages.
The main accusation against cross-server functionality is that somehow the larger population makes people behave worse, because they are dealing with "strangers" from outside their "server community". But actually there is scientific proof that this argument is false. Anthropologist Robin Dunbar showed that in primates (that includes humans) there is a maximum number of people you can have a stable social relationship with. That number, the Dunbar number, is about 150 for humans. Which means that on any World of Warcraft server, even if you only count either the Horde or the Alliance side, the "server community" is too big for a human to remember. Most of the players on your server are strangers to you. Going from a single server to a battlegroup of servers changes nothing. Especially since Blizzard introduced the cross-server ignore functionality: No mentally sane person is sending tells to some jerk he met in a bad pickup group anyway, so ignoring that jerk is all the functionality you ever need.
I believe that the perception some people have that cross-servers make the community worse is just that, a perception, and not a fact. You can't separate people from their wrongly held beliefs, but that doesn't make those beliefs reality. If Blizzard tomorrow switched off the cross-server functionality for the Dungeon Finder, the pickup groups would be exactly as badly behaved as they are now. Only that you'd wait much longer to get into one.