Depth and complexity, yes, yet characters who are too unsympathetic and unlikable are often not "relatable." While most of us can accept a character's flaws if they aren't too severe, there are limits, which vary from person to person. I put up with Stephen Strange's self-indulgent behavior in the first Dr. Strange film because I knew he was destined to become a hero. One of my daughters said she'd had enough of him well before he went to Nepal and won't watch that movie again. (She may not even have finished it the first time.)

I'm not sure where the line falls for me, but most days if I don't see at least some hint of redeeming qualities in a protagonist, I'm not going to care to follow them. I do not relate to people who are completely unlikable and unsympathetic. I don't identify with them. I don't understand them. I don't want to spend 2 hours of my life with them. Some writers may complain about that, but that's how I am, and I suspect I'm not alone.

So sure, depth and complexity, but there are limits to how sociopathic a protagonist can be, at least for most of us.