Tosfos in Bava Basra (160b DH Tiknu) asks your question. The Gemara there says that the Rabanan instituted the use of a Get Mekushar for Kohanim because Kohanim cannot remarry their divorced wives and a Get Mekushar requires a lot of time and effort to write. The hope was that by the time they had finished writing the Get, the Kohen husband would have cooled down and decided not to do divorce his wife.

Tosfos asks why Kohanim today are not required to use a Get Mekushar. Three answers are offered:

1) We don't know how to write a Get Mekushar any longer,

2) The Takanah was only made for that particular place (this is implied by the language of the Gemara there: "in that place there were Kohanim who were very short-tempered"),

3) The Takanah was never instituted as an obligation but only as a possible option.

The fact that the Rambam does not record this Halachah at all implies that he understood the Gemara like the second answer of Tosfos. The Rambam records all Halachos of the Talmud even if they are not practiced today, for example the laws of Techeles in Tzitzis. And, of course, he would have recorded it even if it is only optional and not obligatory. Therefore his omission of the Halachah of Get Mekushar suggests that he held it was a Takanah made for a specific time and place.

My guess is that the Shulchan Aruch omitted this Halachah because the Rambam did.

Kol Tuv,

Yonasan Sigler