I'm beginning to wonder whether there should be any mandatory elements in
the PREMIS schemas, or at least in the Object and Event schemas.

The definition of mandatory in the PREMIS data dictionary is "what a
repository needs to know". It acknowledges that there are different ways
for the repository to know the mandatory data elements and they don't have
to be explicitly recorded. 

So considering the following scenario:

I might make a METS document for what is a set of files, called a
representation in PREMIS, also in my case equivalent to an intellectual
entity. I may want to include some PREMIS metadata about the Object that
is the representation. If I use Object.xsd objectIdentifier is a mandatory
element. But my objectIdentifier is already part of my METS document as
objID, so I have already satisfied the mandatory requirement, but I'm
forced to repeat it in the PREMIS Object metadata. If I also want to
include Event in digiProv to give information about the fact that I
digitized this object, I have to include an eventIdentifier, even
though I don't really have a system that generates event identifiers so
I'll just be making it up to satisfy the schema.

So I wonder if any elements should be mandatory, given the difference in
the PREMIS data dictionary definition of mandatory and the XML schema