I think having coffee together infrequently if she's up for it and being friends are not totally the same thing. She'll never be your bestie but there might be room (like once or twice a year) to go for a walk or have lunch and catch up. I've never really had this with an ex-therapist but have had it with mentors with whom I've had highly intense transferential relationships. The occasional coffee together humanized them a little, made me see them in a more realistic light and helped me see that I'd grown a lot. Without having to discuss our unfinished business, the business was put to rest because I could accept that they were just people like me and see that I no longer needed them in the same way.

Of course everyone is different but I don't think it's necessarily a bad idea to suggest it. It might actually be helpful to you.