This is an interesting thread!
I never even considered asking this question, but I think it's an important one.
To answer your question - yes: I honestly think that I (personally), seek out some form of comfort and nurturing when I go to the hospital while in crisis. Although, it really - IS - the only place to go when in crisis. (Crisis being: suicide) Because it is the only place I can go when I am in crisis - I do NOT look at it as seeking out, "hospitalization," for the sake of being, "hospitalized." Rather, I look at it: like I am in crisis - there is no support that I currently have that can offer the same type of support that a hospital can - therefore, my best and only option quite literally - IS - to go to the hospital.
I recently went to the hospital because I was having suicidal ideation. I did not go with the intention of being hospitalized - I just knew that it was the only place I could go for the kind of help that I required. I could have easily talked myself out of it - and said: that I am not sick enough to go to the hospital, that there are other people who are sicker than me - so I should just go back to bed and sleep it off... But really - that is simply - JUST NOT TRUE. There is a reason why there are psychiatric wards at hospitals and there is a reason why there are outpatient programs. Luckily - for me - they did not put me into the hospital for 30 days, and instead - got me into an intensive 30 day outpatient program - that offers more therapy than inpatient could ever offer. That in itself is important to note - that if there IS something that I seek - it is the means and ability to work on myself - and to have someone to trust and talk to about my issues.
So, to simplify: I would say that I seek out support and nurturing when I am in crisis. Because the hospital offers the closest thing to that which I am seeking - I go to the hospital. However, if hospitals no longer offered the kind of support and nurture that I require - I would go elsewhere.
Hope that helps answer your question.