This is a pointless reason and it’s wrong. Villa, Newcastle and Southampton have all played in the final since 2015. Are you counting Villa and Newcastle as “big 7”?
Why are you selecting a random date of 2015? If you go back three years prior to 2015, then Sunderland, Bradford and Cardiff all played in the final. Two of them football league clubs at the time. If you go back a year before that then Birmingham were in the final.
If you are judging a chance of win on history then what’s the point in playing football? We hadn’t won the league before we won it.