Why do you (or these indexes I suppose) think that a pure parliamentary system is a better system?
A better question to ask might be: why do parliamentary systems score so high? Also, why is proportional representation so good?
I will speculate, but some of these speculations are based on what I've read.
An important virtue in democracy is willingness to be a good loser. It is easier to be a good loser if one does not lose all that much. That also limits winners, since their victories are are only partial. That's an advantage of ruling councils and legislatures over single rulers, because each councilmember is one of many. Proportional representation increases that advantage by avoiding all-or-nothing outcomes for individual seats; a party can get representation even if it would get shut out of representation in single-member-district elections.
There are non-proportional ways to do elections to multiseat bodies, it must be noted.
- Single-member-district elections
- Bloc vote -- vote for some number of candidates up to the number of seats
- General ticket -- vote for complete slates of candidates in single-winner fashion