I have looked at the entire 1970s decade. These are the top four each year and finishing positions of the modern day big six. There really was no cartel dominating to get past. Checking this made me realise how shit Arsenal were for a good chunk of the decade too!
1969-1970 Everton, Leeds, Chelsea, Derby (Liverpool 5th, Man U 8th, Man C 10th, Spurs 11th, Arsenal 12th)
1970-1971 Arsenal Leeds Spurs Wolves (Liverpool 5th, Chelsea 6th, Man U 8th, Man C 11th)
1971-1972 Derby Leeds Liverpool Man C (Arsenal 5th, Spurs 6th, Chelsea 7th, Man U 8th)
1972-1973 Liverpool Arsenal Leeds Ipswich (Spurs 8th, Man C 11th, Chelsea 12th, Man U 18th)
1973-1974 Leeds Liverpool Derby Ipswich (Arsenal 10th, Spurs 11th, Man C 14th, Chelsea 17th, Man U 21st (R))
1974-1975 Derby Liverpool Ipswich Everton (Man C 8th, Arsenal 16th, Spurs 19th, Chelsea 21st (R), Man U Second Division)
1975-1976 Liverpool QPR Man U, Derby (Man C 8th, Spurs 9th, Arsenal 17th, Chelsea second division)
1976-1977 Liverpool Man C Ipswich Villa (Man U 6th, Arsenal 8th, Spurs 22nd (R), Chelsea second division)
1977-1978 Forest Liverpool Everton Man C (Arsenal 5th, Man U 10th, Chelsea 16th, Spurs second division)
1978-1979 Liverpool Forest WBA Everton (Arsenal 7th, Man U 9th, Spurs 11th, Man C 15th, Chelsea 22nd (r))
So Liverpool were in the top four every year from 1971-1972 until 1978-1979, and the lowest they finished was fifth in the entire decade.
Arsenal had one title and one close championship challenge. The rest of the years they missed the top four
Man City one title challenge, one other top four finish, and, the rest is mid table at best
Man United one third place finish, the rest nowhere near, and one relegation in the decade
Spurs no top four finishes at all, and only one year even really in the shake up, one relegation
Chelsea one top four finish, no other appearances in the European shake up, two relegations and stayed in the second division for two seasons on the first relegation.
The cartel at the top just didn't exist like it does now.