Every 401k or other investment place I've seen allows either taking dividends or reinvesting them. I've never one seen a fund that picks only divide free or divided providing stocks as a choice.

And every big fund also provides all sorts of general index funds, which certainly contain both. And individual stocks themselves decide to pay dividends or not, and routinely change so.

I don't think your distinction is at all a relevant factor in these funds to nearly any end buyer.

Please provide a citation as to why you think your claim is true.