This is something I've thought about throughout the past few months when I was almost hospitalized a few times. I think if I were in the hospital (for MH reasons, not just a physical injury), it would be really nice and helpful to me for my therapist to visit if she could, or even just call me.
Also at my clinic they offer "crisis" appointments but it's really if you are in CRISIS (ie about to self harm or commit suicide) and they place you with whoever is available, not your own therapist. But my therapist once called me personally (usually the clinic calls) and offered to come in an hour early to give me a session the very next day, because she had heard about a traumatic experience I went through. I appreciated her going out of her way to do that for me.
Both of those things I believe are within ethical therapist-client boundaries.