Ah, yes, cap weighted would tell a different story: if you can’t or don’t want to pick stocks, buy the cap weighted S&P 500 (or some other index you like). You’ll do best over long periods of time. Period.*
Going back to the original ask “Only invest in shares that pay no dividends” would be picking stocks, though - i.e. the Dividend Non-Payers (or worse, including the Dividend Cutters & Eliminators) …this passive ETF doesn’t exist for a reason.** And we’ve come full circle. 
* Outperforming or even just matching the index isn’t always the goal, though. Perhaps one wants to maximize tax efficiency, as the originator of this thread, or better than index yearly cash flow / dividends to offset current expenses (as I aim to do). Active investing can help achieve those goals. Sometimes it even beats the index significantly.
** Imagine you want to launch a new passive ETF or mutual fund with “companies that pay no dividend (or have cut or eliminated)”. Do some backtesting and you’ll quickly conclude “no way” (not saying that past performance is indicative of future performance, but backtesting is just on the 101 list for portfolio management - unless you are Cathie Woods, of course).