Earlier quoted context omitted.
Why would that matter? If they are obligated by their funds' charters not to intervene, then all the governance decisions happen exactly as if they hadn't invested, right? 10% vs 90% of share votes being on auto-pilot shouldn't matter? Is the argument that the vast majority of them could change their funds' charter to allow them to be actively involved with governance? If so, that would be really hard to achieve even…
If 90% of shares are non-intervening that means hostile takeovers are now 10x cheaper to implement. It would be weird to be a company with market cap $100M, where $10M could buy a controlling interest in voting shares.
Naively (ignoring other dynamics of index funds), sure, compared to 100% investors actively engaged in governance. But I suspect investment in index funds replaces largely hands-off direct investment and so, market wide, has virtually no average effect on that (though it may shift the effect among firms compared to those investors doing so directly.)