This implies also that I don't use POD::Coverage.

There is no reason you cannot still use Pod::Coverage. All you need to do is to tell it the methods which you decide are private, and it will skip them. You basically just pass in one (or more) of these options to the constructor:

private an array of regexen which define what symbols are regarded as private (and so need not be documented)

also_private items are appended to the private list

trustme an array of regexen which define what symbols you just want us to assume are properly documented even if we can't find any docs for them

And of course all these options are available thougth Test::Pod::Coverage as well.