Cavill playing hardball because he knows WB doesn't want to lose another cast member that will further endanger the status of the DCU. Even with Affleck out WB is committed to Wonder Woman 2 and Aquaman. They really don't want to give up on their JL movies just yet and keeping Cavill is vital to that.
He had some leverage during the CGI mustache phase, before JL dropped. He has no leverage now.
Cavill must think he is in the MCU, not DCU. He better be careful. He might get Ed Norton'd. Justice League is not Avengers....on film. Justice League was dead on arrival. The people had enough, the turnout showed that.
The only thing alive in DC is Wonder Woman at the moment.
If everything else was scrapped, that would be a start to something fresh. That is what the people want.
A JL movie that the public would want to see, would mean they've established more than one character outside of Wonder Woman. A large part of Avengers' success is the list of well-received solo MCU movies leading up to the Avengers movies.
JL future success depends much more on that than Cavill.