Zero-frets can be found on a number of very expensive basses and headless guitars, but they have never quite made a real breakthrough - though undeservedly so, as some guitar-builders would agree, considering the fact that they provide for an ideal string height over the first fret, which leads to fewer intonation problems.
Another advantage sometimes mentioned, but probably neglectable, is the absence of differences in sound between open and fretted strings due to the use of different materials for the frets and the nut.
Using a zero-fret is in many ways similar to putting a capo on the first fret and does work well. The strings rest on the zero-fret, and the nut, which is placed about 5mm (3/16") behind the zero-fret, only serves to guide the strings. Worn zero-frets can be replaced just as nuts can. To make a future replacement easier, you can make the zero-fret slot slightly wider.
There's no reasonable reason that speakes against a zero-fret. It's just tradition to use a nut.