"if you keep doubling-down on positions that are losing, eventually you'll blow all of your money on something that never recovers"
I partially disagree. If a big company, one that is not in trouble, reduces 50% in value for no apparent reason at all, it's may be time to buy. Just don't completely forget diversification.
Usually, such reductions of value happen only when the general trend of market is down. It is hard to find stocks 50% for sale when stocks of other companies are not for sale.
The wisdom here is that usually there is a reason for a particular stock to reduce in value. You'd better be aware what the reason is.
For example, I can't see how you could ever go bust dollar-cost averaging on a big index like the S&P500
You can go bust. Invest too much, ignore the recommendation to keep an emergency fund. Then you may have to sell the stocks at lowered prices.
The market can stay irrational longer than you can stay solvent.
But, in principle, you're right. Buying S&P 500 index is nearly equivalent to buying stocks of Corporate America, if such thing was possible. The S&P 500 has a certain dividend yield. The investment is inflation protected. Also, you benefit from GDP growth by having a certain share of Corporate America.
From this, we can calculate the expected return. For example, dividend yield can be 4%. Inflation can be 2%. GDP growth can be 2.5%. From this, you get 8.5% return. Plug in your best estimates for dividend yield, inflation and GDP growth and you get best estimate for the return.
The trouble is, this return is guaranteed only on the very long term. If you do a short-term investment, then the valuation difference between the time of purchasing and time of sale makes a large percentage of your return. In such a short-term investment, your return could even be negative.
The benefit of dollar cost averaging is that you diversify in time. You buy stocks when they are expensive, but you also buy stocks when they are cheap. You get more stocks when they are cheap, obviously, so such purchases make a majority of your return.