Increasing diversification reduces specific risk, but you're more likely to be increasing your exposure to broad systemic risk. It's like the idea of an MBS. Diversification was the argument underpinning that: buy a portfolio of a ton of mortgages and you'll never have to worry about the quality of any individual mortgage. But when the housing market collapses systemically, you're toast. Alternative to the MBS, you could buy select high quality mortgages, where you may not have the same systemic risk (though now your skill is in question). 

But at the end of the day, indexes or broad portfolios are all about individuals in aggregate, and quality does matter. You can pretend it doesn't, and that's the mainstream advice these days. And perhaps this ignorance even makes sense, as few managers have proven capable of outperforming sheer ignorance. But it is an ignorant view. Indexing is buying garbage, it's assured. You're just hoping the garbage is specific and not systemic.