Not the vice president, mind you--the office of the vice presidency. So advises Reason magazine contributor and vice presidential historian Jeremy Lott in the Washington Post. His main reason: it leaves people who would not normally otherwise be considered fit for the job as president, either as direct slot-fillers or as unfortunate legacies.
Lott doesn't declare what alternate means he would use to fill the post when the president we've got leaves us, but I might entertain such options as having the caucus of the party controlling Congress (or that of the party from which the president came) picking one.
Or maybe as much as they tend to suck, vice presidents are a necessary evil for that filling the vacancy role. Lott does suggest that if the office isn't eliminated, it should at least be voted on separately. I'm partial to returning to the original idea for the office in the Constitution: that the presidential runner up cop the post.