What's fun when playing in the Byzantine Empire, no matter the bookmark, is precisely the "game of thrones". If you don't enjoy the risk of losing the prophyrian throne to a powerful strategos, Byzance is probably not the best pick for you.
I know some people will tell you that you can prevent anyone else to access the throne, but by doing that you would just avoid what makes the Byzantine empire different from all other empires.
I find it more fun to have to step down from time to time, so you can reconquer the throne (peacefully or not) when you have a worthy character. It's not even roleplay, it's just that playing an an invicible emperor is boring.