My T would definitely react like yours or maybe even say no but let's talk about why you want one- are you trying to take over the role of T? I don't think he immediately conjures up a scenario in his mind in which a patient is deeply emotionally attached to him, as he views himself as a doctor. He doesn't think in terms of relational as a first inkling or even fifth. He sees himself entering into the patient's world and improving things within that, not becoming a part of it.

He has written a few heartfelt and charming few-line emails over the two years, and they might in some way be a transitional object for me(?).