Earlier, wrote:

...In addition, you've got the prop
spinning at 3200 rpm...

Well, that's one of the things that makes hydraulic drive sort of
compelling: There are plenty of variable displacement pumps that will
give you infinitely variable ratios. So there's no reason at all why
you would be constrained to 1:1 drive. Or even to any fixed ratio. And
the pumps and motors developed for airline and military aircraft
application offer some pretty good power/weight ratios. We're not
necessarily limited to the cast-iron lumps that Grainger sells for use
in industrial trash-smashers and the like.

...There will also be the weight of
the oil lines...

Well maybe the weight of the oil lines would be compensated by the
absence of shafts, belts, gears, etc...

One possible application might be for driving remotely-mounted
propellers for unconventional configurations, as the OP suggests.
Sure, for your typical aircraft of conventional configuration, direct
drive will probably continue to be best way to go. But perhaps for
retractable-propeller self-launch sailplanes, and other odd layouts,
the advantages of hydraulic drive might outweigh the disadvantages.

Bob K.