I love doing dungeons in a group, but being able to solo them really adds something to the game, for three reasons.
The first is that it makes the world bigger, and more connected. When you have to wait in a queue to enter a place, it does not feel like a part of the game world. With a soloable instance, you can simply walk to it and enter it, with the usual loading screen. Just another zone in the world.
The second is that it adds a single-player game experience. You fight scary monsters on your own, and are the tank and healer of yourself. That really kicks in when you start to have challenging solo encounters. My fight with Isgebind at the end of Stone Vigil ranks among the most fun I ever had in a game. It also gives even more meaning to becoming stronger. The stronger you are, the higher level dungeons you can tackle.
The third is you can really explore dungeons, stop when you wish to, look around, smell the roses.