Rose = (Susan + Ian + Barbara) x 2005
Somebody like the Doctor – an ageless, lonely wanderer – he can’t be that desperate can he? You would think that with his wisdom and experience, the last person he would want to get his leg-over with was Rose.
Since that’s the same thing as love, yes.
Rose “saved” the Doctor when he was at his most vulnerable, his most miserable. Therefore, he became attached to her in a way he rarely allows himself to become attached to others. She became attached to him because, well, she’s a silly little kid and he showed her the world. Though in the short term they bettered each other, eventually the two of them had to part ways — for reasons illustrated in both School Reunion and Girl in the Fireplace (the one on Rose’s end; the other on the Doctor’s).
The Doctor’s fixation on Reinette, if anything, helps to illustrate the nature of his relationship with Rose. All it takes is that rare person at the rare moment who can break through and touch him, and he’ll latch onto her. Rose did it by being stubborn at the right time, then worming under the Doctor’s skin, showing appreciation, nurturing him. By giving him a certain regularity, and a family of sorts. Reinette did it by literally crawling into his head, seeing things that he normally doesn’t show anybody. When he lost Reinette, and he reacted that badly after having only known her for a few hours, that set up just how much of an effect it would be on him when Rose left.
At least Rose is safe, though. In a way he gave her what she always wanted, before he came around — and what he could never have. Though the TARDIS will feel very empty for a while, the Doctor will… well, not get over it. He’ll put it behind him, though; chalk up the sadness to just one more illustration of his curse — how alone he innately must be — and move on. It’s kind of like ditching Susan all over again.
I don’t think we’ll see him that ga-ga over another companion. I get the feeling the Doctor isn’t about to be so dependent on anyone again, if he can help it. At least, that’s the way he always used to work.