My two biggest concerns would be 1) how does the ER of this hypothetical fund compare to a standard index fund? and 2) how representative is it of the overall market as a whole?
1). S&P 500 currently has a dividend yield of 1.90%. On qualified dividends, you might end up paying 23.8% if you are in a high enough tax bracket. If the alternative "low dividend" fund cuts your dividend payout in half, that means an increase in expense ratio of even 0.27 percentage points is enough to wipe out any benefits from tax savings. If you find a "no dividend" fund, it takes a larger increase in expense ratio to completely wipe out the tax savings, but it could still cut into them significantly. And a no-dividend fund makes the potential for #2 even worse.
2) Naively excluding companies that pay above average dividends (or any dividends) would likely mean your index would be very underweight for economic sectors like "Basic Materials" "Financials" and "Utilities" where higher dividend payouts are common. You'll also tend to be overweight big tech stocks that don't pay any dividend at all (think Google, Facebook, and Amazon). For the last couple of years being overweight in those several stocks would have been a winning strategy. It may or may not continue to do so.
People can do some complicated uneven weighting to try to replicate the sector distribution of the overall stock market even though they are investing in a small and non-random subset of the companies in the index, but that will tend to make #1 even worse.