The best evidence for this comes from Scott Keller and Colin Price, authors of "Beyond Performance: How great organisations build ultimate competitive advantage and the reason that it’s important is that both authors and senior consultants at McKinsey.
This is the way McKinsey describes their concept of organisational health / capability:
“The pace of change is faster than ever, so organisation’s ability to adapt is more crucial than ever. Furthermore, information is so readily available that most aspects of any organisation’s competitive advantage can be fairly easily copied by competitors. What can’t be so easily replicated is the ability to grow from within through better ideas and better execution, ie better health. This is why the authors call organisation health ‘the ultimate competitive advantage’. And healthy organisations’ success isn’t in business alone: They serve a greater good, enabling workers to unlock their full potential in the workplace.”
And see this video with the authors, and note their quote that:
“Performance is very much about our strategy, the big goal we’re going for that we can measure in financial terms, the set of initiatives we’re going to go after, the sales force stimulation programme, the lean production programme, whatever bundle of things they’re going to do in order to get to those numbers,
The health side is very much about me - how well do we align people on where we want to go, how efficiently do we execute against that, and how effectively, and how do we renew ourselves along the way, keep our energy up and be able to continue once we even get to that target.”
Organisational health is organisational capability and it’s not just HR saying that it’s important - the premier firm of strategic business consultants says so too.