I too would ike to see a config solution to this. I have many post types which populate a custom template, are set non-public to disable the single view, and as a result I’m not able to use ICPO with them.. SO i end up having to toggle them to public every time i want to resave ICPO. I’ve seen other plugins do this too, and while its a neat way to get rid of post types like Attachments appearing in the list I think there are very legitimate uses for CPTs being non-public.
Surely it would be better to use an array filter to extract post types like Attachments etc from the CPT generated list, rather than blacklisting all non-public types… Or just have a toggle checkbox to show/hide non-public CPTs…
