We just had one become a elder which mean they also have tied to political aspect of the world.
That's called a promotion. It doesn't mean Garling had a politics focused role beforehand, his role was mainly military, as a knight.
Not even the FA can order around the HK and they have deal with issues within the hoy land for CD.
Yes, they work under a different branch. That doesn't change that they're a military force sent to conquer countries for the WG(for example, Elbaf)
There more than just another another military force for elders\Imu .
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Because they're CD's? Sure, but that doesn't change that they do ultimately serve as Mariejois army.
Still when Oda said that line in the manga there was most likley no HK in his mind since that was 20 plus years ago lmao.
No matter how weak or strong they are .
Unless there's something new in the manga that contradicts the statement, there's no reason to think the admirals aren't the WG's strongest military force.