OTL, many folks in 1841 thought John Tyler as only Acting President and argued that a new election should be held. There wasn't really a way around the fact that Article II is pretty clear that the Vice-President assumes power.
While a special election would be expensive from a simple financial point of view, it would allow for a bit more democracy: an election by Congress of the President opens a huge can of very dangerous worms -- the expereinces of 1800 and 1824 suggest finding a way around the situtation is preferable.
Indeed, if special elections had been used, perhaps they could have used in 1876 and 2000 as opposed to Congressional or Judicial chicanery.