The reason pension funds include index funds in their mix of investments is because those funds have two features that are exactly what pension funds are aiming for: (1) broad diversification, and (2) conservative inclusion rules that avoid undue exposure to highly volatile firms.
Changing one of those features undermines the reasons for including the index. Doing it specifically for the purpose of including a firm where large pension funds have also been extraordinarily critical of the governance structure as a particular source of risk [0] even moreso.
[0] https://www.reuters.com/legal/government/new-york-california...
I was looking at it from a more institutionalized perspective I guess. At least in my field, I know how this works because I see it play out. People are conservative and sometimes would rather be wrong with the herd as long as it means they're not risking being wrong on their own.
Having said that I guess you have a valid point. Once major institutional investors decide an index has basically gone corrupted, then they won't actually buy the index fund anymore. They will just buy all the stocks in the index, and underweight the parts they think are tainted. That's what I would do, anyways.