I would have thought that that would always have been a consideration.
Oh, to a certain extent, I suppose it has been. Veeps probably were more carefully chosen after the Kennedy assassination too. But as time goes on and we feel pretty safe, they feel free to choose a VP solely because of their state, or other single issue type things.
I don't think anyone was seriously concerned about Cheney and his health problems and the effect they would have if he had to assume the Presidency. The media splashed it around because they could. It's just not much of an issue these days.