I believe the idea of the permanent plate for fifth wheel and gooseneck trailers in Missouri is because we pay a plate regis fee for the truck that is based on the total GCW of the truck and trailer. So we have effectively already paid the "road use tax for the trailer" in the registration of the tow vehicle. The fee for the one time plate on the trailer is essentially a document fee.
We have the perm plates on our horse trailer and equipment trailer.
To the OP, the Missouri State park at Weston Bend is very nice.