Protected and private methods are not part of the public API of a class.
There are many reasons for keeping methods away from end users. Usually they are internal helper functions that are simply too low level to be useful to be called by the end user. Sometimes they are not public to keep the interface simpler. Non-public methods also advantageous because library maintainers can change/remove them without worrying about backward compatibility.
VTK widgets have many problems. They are one of the very few parts of VTK that I would not recommend anyone to use.
Anyway, if there are specific methods that you wish were public then let VTK developers know.