It doesn't.
Over the last 10 seasons (going all the way back to the 72 point
@davek season), here's a breakdown of which non-sky6 teams finished between 1st and 6th:
22/23: Newcastle, Brighton
21/22: None
20/21: Leicester, West Ham
19/20: Leicester
18/19: None
17/18: None
16/17: None
15/16: Leicester, Southampton
14/15: None
13/14: Everton
Over 10 seasons, the 60 top six positions have been filled by a non-sky6 teams 8 times.
The only club who have 'regularly' finished in the top 6 are now in the Championship.
Any sky6 club which misses out is invariably back in the top 6 the following season.