Should I be worried about my boyfriend's close female friend?

Anonymous
So my boyfriend of one year has a close female friend lets just say Amy. He and Amy used to work together at his past job and have been friends probably a year before I met him. This means they've known each other for about 2 years. I am worried for a few reasons:

1. I looked through his phone at their old conversations and he used to ALWAYS like every day ask her to hang out, he'd visit her at work. I feel that he's never made a move is because she's always had a boyfriend.
2. My boyfriend puts extra effort into their friendship; With his other friends, he doesn't ask about their lives, doesn't initiate conversations, they're just friends he smokes with. But with Amy, he makes the effort to check in on her, he is always the one to initiate plans with her and message, even though she doesn't make the effort to keep in touch with him.
3. They only hangout one on one. She's not in his life because they have the same circle of friends, she's literally just someone he chooses to keep in his life. Whenever they hang out, it's one on one and they treat each other to dinner and movies.
4. He has had other close female friends in the past, yet he's chosen to cut them off, but not her. With his other female friends he never made the effort to commute to them (he doesn't drive), he doesn't ask them to hang and he rarely checks up on them.

My boyfriend has been very honest about their friendship, and he tells me every time he hangs out with her. He tells me he's not attracted to her and he sees nothing but a friend from her. They only hang out about once a month and they text here and there. I'm just worried as to why he's chosen to invest more effort in his friendship with Amy, moreso than any of his other friendships and why Amy gets special treatment that none of his other "close" female friends have gotten from him. Makes me feel like he's keeping her around in case him and I don't work out. He knows their friendship bothers me but just keeps reassuring me it's nothing
Updates
+1 y
Do you think he's only dating me because she's taken, and that something may happen when she's single? Do you think she's a backup for if him and I don't work out? What should I do? I'm certain he will never admit feelings or intentions towards her...
Should I be worried about my boyfriend's close female friend?
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