Why is my Custom Pawn unable to be controlled or moved?

As far as I know, you can’t change the shape of the collision component of a DefaultPawn using only Blueprint. You’ll probably have to go with inheriting your blueprint class from Pawn. As you point out, there is no default collision component. But you can create one!

Using Pawn as your base for your blueprint class, go to the Components tab. In the Add Component drop down, select Box under Shapes. With the Box as your RootComponent, I would then add the StaticMeshComponent as a child. As for defining your collision behavior first you’d want to size/position the box to match the shape of your paddle mesh. Next, edit the properties of the BoxComponent to define your collision behavior, possibly using one of the presets. (If the DefaultPawn collision behavior was fine other than the shape, I’d select the Pawn preset.) Finally, set the collision preset for your StaticMeshComponent to NoCollision, since you are already driving collision from the BoxComponent.

Here is a screenshot that might help you (I scaled both the BoxComponent and the Cube StaticMeshComponent to match each other and look like a paddle):