My router plane was inherited from my great grandfather, and doesn't fit any of the above styles listed.
Effectively it's two blocks of wood carved to be easy to grip which screw together (with woodscrews) clamping the blade in place. The blade itself is little more than a broken off chisel blade which has been tidied up and sharpened to suit the angle it's held at.
There's a shallow recess carved into the front face to give you some visibility of what the blade is doing, but no holes etc.
I'm presuming it's mostly due to being used to it, but I can't imagine using any other style of router plane now, although would definitely consider a metal version (just because the use of woodscrews is a weak point which I've seen cause other old tools to fail).