You've got that wrong. Back to back CL titles have been done before (not by us, granted). No one has won 4 PL titles in a row before.
Liverpool won back to back European Cups when the competition was much weaker than the CL. No English team has won back to back CL titles, probably because the competition is much stronger than its previous incarnation. Even Pep's Barca or Bayern couldn't win back to back CLs.
Both 4 league titles in a row and back to back CLs would be some achievement. I'd be happy with either. But I think the players prefer the CL, let's say because it brings more prestige. Milan 88-90 are considered among the greatest teams partly because they won back to back European cups. Think only Real have won consecutive CLs.