I'm sure that the reason for standard guitar tuning being in fourths instead of fifths is a matter of just scale length. Fifth tuning would place first position notes at the fifth and sixth frets which would be beyond the stretch of most players. It's the same reason why the bass violin is tuned in fourths while the rest of the violin family is tuned in fifths. Generally speaking, the scale length of an octave mandolin is about as long as most people would want to deal with in a fifth-tuned instrument.   

Conversely, third tuning would lower the number of available first position notes considerably. Third tuning starting with the same low E as standard would be EGBDFA, with that high A being the equivalent of third string second fret in standard tuning. That would put the E which is standard's open first string at the 7th fret.

Bruce