Very strange solution you are bringing up.
This solution is not a solution of your problems at all. It can, on the contrary, turn out to be an aggravation of them.

A true solution would be trying to step out of your depression. Little steps, baby steps, but doing something to be able to meet your lovely friend on some other grounds than your depression.
That would really be a reward to her, not cutting her off!

Why don't you believe her when she says that she cares very very much about you?
You think that she may mean it, but I would take the sentence quite literally and be very very happy about that.

When I was depressed I couldn't believe that other people would see some good in me. I felt like a wretch and i thought that it was all it showed.
I was wrong.
I always had friends and people loving me, in the while, but as i was not loving myself i simply could not believe they were really caring for me.
But I tell one thing: even when we are sick, what we really are shows out. The sickness shows out too, but also who we truly are. And that's what she loves about you, who you truly are, because she can see it.

Do you really want to reward a sincere friend, who's always been by your side, by cutting her off?