If you haven't noticed, there's a certain relevance to the devil fruits.
Logias are only held by people of Whitebeard's crew and high-rank Marines, the exception being Crocodile and Eneru, but Eneru doesn't really count and that only supports my theory of Crocodile being a former part of Roger or Whitebeard's crew.
Zoan are only held by bodyguards and people associated with the WG, the exceptions being Chopper and Lassoo. Though in Chopper's case, it's entirely possible that his Zoan was intended for Chessmarimo and somehow was lost in transit to the castle.
I might suggest you've got it backwards. Once you get a DF, it provides you with such a profound benefit, those positions become logical ones to reach.
If you get a Logia, it pretty much allows you to power past almost any competition for rank or power.
If you get a Zoan, it enhances the skills which would be desirable for bodyguarding.