To be honest the true reason (in my opinion at least) why MNK in the current state is not popular (and will never be, if they don't revamp the class completely so that they have lower personal DPS but bring some sort of raid-DPS increasing ability to the table) is that most raiders care a lot about their personal DPS (even more so in hardcore groups).

Way too many times have I seen groups, even on the casual or midcore end of the spectrum, recruiting exclusively DRGs or NINs for their groups, without even considering MNK as a solution, just because the majority of the people in the group want that "DRG NIN" composition to boost their personal DPS and be slightly higher on the FFLogs DPS list. Even if that means refusing a godlike MNK in their group that would make them have higher raid DPS, or having the MNK switch to DRG or NIN even if they play those classes very poorly compared to their main.

In the end people just want their own selfish "number" to be higher.