hi dave. Apologies for the slow response - i've been on leave. Certainly - the Human Learning Systems case studies collated here (https://www.humanlearning.systems/case-studies/) provide significant evidence - particularly the Plymouth Alliance: https://www.humanlearning.systems/case-studies/#plymouth-alliance232 and the Gateshead/Changing Futures work: https://www.centreforpublicimpact.org/assets/pdfs/hls-practical-guide-gateshead-casestudy.pdf
These case studies are discussed at length in a practioner focussed context here: https://realworld.report/, and in a more public management academic context here: https://policy.bristoluniversitypress.co.uk/harnessing-complexity-for-better-outcomes-in-public-and-non-profit-services
The causal link between creating learning systems and improved outcomes is also the conclusion of a soon to be completed PhD (which the candidate shared with me recently), and was the subject of a number of the presentations at the recent Relational Public Services conference in Newcastle in June: https://www.complexityoutcomes.org/
Hope that helps - very happy to chat further about all this.