Ok so having just watched a Vineyard Valentine and seen Luke's attitude to Logan and having seen Luke's behaviour towards Dean in We Got Us a Pippi Virgin, does anyone else think he's incredibly overbearing and rude? And his interest in her boyfriends is possibly bizarre?
I don't buy that the whole thing is about how she's like his daughter etc. Even Chris her actual father isn't that bad (except when drunk ie Wedding Belle Blues). And the writers seem to be in flux over how much of a presence Luke was in her life. In season 7 he's like the father she never had, but there's other references about how he's just the diner guy and how they only really moved to Stars Hollow when Rory was 12. It's weird and his behaviour towards her boyfriends is very puritanical.
I also don't buy into the idea of Luke as a kind of surrogate father to Rory. I used to think along those lines but not anymore. He is sincere in caring about her well-being, i don't doubt that. Nor do i doubt her fondness for him. He cares for her as an extension of his feelings for Lorelai. Rory can see that Luke cares for Lorelai and he has been there for her, for example when he dropped everything to drive her to the hospital when Richard was ill. But it doesn't go much deeper than that on a personal level between them. I put Luke more as a doting uncle to Rory. There is not a bond between them in the way Rory has (or wants) with Christopher. I don't think Rory was looking for a replacement dad; she wanted Christopher to fill that role for her. Rory would have been happy to have Max as a step-father if he and Lorelai had gotten married, but i never felt that Max would have been a kind of replacement for Christopher either, more of an addition.
I think Luke views Rory as a sweet, intelligent, innocent girl. He doesn't know her well enough on a personal level to see beyond that ideal. He knows her more on a surface level, not any deeper than that, and perhaps that ideal prevents him from accepting her with any other guys. Luke did like the idea of Rory hanging around with Jess, but not for Rory's benefit. She was hoping Rory's influence would help Jess get his own act together.