One thing that seems to work fairly well for me is clearing all cookies/temp files with ccleaner, starting firefox and going to Saints Row page on the store, log into account, accept cookies and the mature warning, then try starting the game up.
I don't know how that's actualy working at all but I'm regularly getting the game started doing that. You'd think that the epic launcher alone would be fine, but maybe it's recognising that I've logged in to the store on a browser for some reason and then the game starts.
I really hope they get it sorted out soon though because it's stupid obviously.