Yes, I think it's partly this extreme pre-occupation with the
afterlife, and the fear of suffering in hell, that makes many
Christians want to spread their religion to others, so as to "save"
them from eternal damnation. But all this fire and brimstone talk
just sounds rather paranoid and irritating after a while.
Regarding the preaching by hospital staff and unsolicited visits by
proselytizing groups, I think it's really despicable in a way, in
that they are preying on the vulnerabilities of people who are sick
and/or dying. They are making use of their immediate fears of the
imminent afterlife to make them convert to another religion.
Perhaps the proselytizers really preached with sincerity and
earnestness, but it just somehow doesn't feel right to me.