Adding a group finder without causing the consequences that WoW's dungeon finder came with could perhaps be done in some way. If it could be done without causing those problems, I wouldn't mind it at all.
These are the consequences that I would like to be avoided:
1. "Heroic" dungeons being too easy.
In order to make the dungeons doable for a uncoordinated groups of strangers, blizz made them extremely easy. And there was no alternative for those that wanted 5-man content to be challenging.
2. Lack of variety in terms of difficulty, length, amount of trash, nr of bosses etc.
All the new dungeons in wow are equally easy, roughly equally long, roughly the same amount of bosses and trash. To randomly be assigned a very hard dungeon, or a very long one would probably just be a pain. But the "solution" to simply not make such dungeons isn't very good. I'd prefer to have variety. Short ones, long ones, easy ones, hard ones.
Just so you understand where I'm comming from: I don't like to spam trade for groups, nor do I like to queue up for zergable content. I play with my friends, some of which I found in the game, some of which I brought to the game and some which brought me to the game. The argument "if you don't like dungeon finder, you can still form groups by spamming trade or play with friends" works for how groups are formed, but it doens't apply to the variety, difficulty and sense of progression. And THAT is what I care about.
I'm perfectly alright with having a bunch of equally long, easy zergable dungeons in a PUG-finder system. As long as I get a few that are fun and challenging, worthwhile the time just for the gameplay itself for a well coordinated group using voice-chat, knowing eachother etc.