I suspect you have not filed because of what you have said about how unfair post divorce life is for women in Greece. The lady that cares for and teaches my kids on Friday is from India and she was quite shocked at how my X got so rewarded and I got financially punished for her adultery that ended our marriage. She told me that in India, the woman gets nothing even if it is not her fault. One thing is for certain and that is "Life is not fair".
I think a reason you could justify for filing would be that you would want to start dating to meet someone new. Other than that, what is so bad with continuing on in a "hidden divorce" marriage? If nothing else, it is good for the kids.