I like the Theurge wizard. First, I like the idea of character background of a character besides a cleric having their faith as an integral part of their identity and a source of power and influence on their skill set. Second, I think wizards as a character-class make a good match with a divine domain. There is certainly plenty of examples of wizards in fantasy literature with a spiritual, divine, or religious component. Third, it is a thematically appropriate way to give wizards a heal ability (I know there are various necromatic and "blood magic" spells that give heal abilities, too). I don't understand why clerics need to be the official "healers," not does it sound interesting to play a cleric as a "heal bot." Also, other classes have heal abilities and there are fears you can take to get heal abilities, so I do not see why people are concerned about the wizard getting some heal abilities. Fourth, since wizards have a special background in magic, I see no problem with giving certain cleric domain features to the wizard early at level 17. They get everything else LATER than a cleric would, so yes, there should be some sweetener to choosing this subclass, or else why bother? Fifth, who cares that wizards have already have access to lots of spells? Many of the official spells are weak or only useful in very specific situations. And, remember, you have to prepare spells in advance, which limits the benefit of having access to lots of spells. People throw silly fits about the wizard class being "overpowered" when there are so many magic-user classes now--nearly everybody and their mother can cast spells, and the wizard class lacks combat skills, has to prepare spells, and ultimately doesn't outperform many of the other classes as one progresses through the levels. Sixth, the Arcane Initiate feature really is not that great because you have to take all the spells in your domain before you can choose other cleric spells. Many of the spells in many of the domains already ARE wizard spells, which means over the long course of leveling up, you are really only getting a limited number of cleric spells that you would really want. I would personally get rid of this "fill up your domain" requirement, as it would make this subclass easier to manage and more desirable to choose without really giving that great of an advantage.
All in all, I think this is an interesting wizard subclass that would be fun to play and add some flavor to a campaign. I do not see any problem with this subclass if it is played right and managed by the DM. And, as always if you don't like it, then don't use it in your game, but I see no reason why it should not be an "official" option for others to play.