I generally agree (and whichever is easier get bonus points, of course).
But just to wrap things up on my end, I did a run through S&P 500 from 1 January 2000 to 1 December 2019 (making sure to hit the 2008 crash). On the same assumptions as previously, the average figure for a DCA person through this period would be ~1,571.77 whereas culepico's methodology results in ~1,577.79. That means ~105.55% returns for the former and ~104.77% for the latter. Difference is truly slight (but the DCA results, I think, lends support against the alleged efficacy of culepico's methodology).
I am piqued by both methods and had time to do further calculations (using S&P 500 historical chart).
First case, same scenario as you have calculated above. Monthly DCA at the opening price from 2000 to 2019.
Blind DCA: Average buy price = 1,571.77, total returns = 105.55%
DCA up: Average buy price = 1,577.79, total returns = 104.77%
Blind DCA has the edge.
Second case, to smooth out volatility. Weekly DCA at the opening price of every Monday from 2000 to 2019.
Blind DCA: Average buy price = 1574.88, total returns = 105.74%
DCA up: Average buy price = 1573.10, total returns = 105.97%
DCA up has the edge.
For dividend paying ETFs, assume $1.50 per month per $1000 invested. Also assume that there is a $1.50 brokerage fee per $1000 per trade. The dividend yield and brokerage fee cancel each other or are negligible, so there are no effects on the numbers for the above analysis. For non dividend paying ETFs, you have to take into account the brokerage fee per trade.
My assumption is that for less volatile trends (or more regular DCA), DCA up > DCA blindly. The reverse is true for a more volatile trend.
So I did an overly simplified simulation.
First case, more volatile trend over 20 time points. Prices as such: 1,2,3,4,5,6,5,6,7,8,9,8,7,6,7,6,5,6,7,8.
Blind DCA: Average buy price = 5.8, total returns = 37.93%
DCA up: Average buy price = 5.9, total returns = 35.59%
Blind DCA has the edge.
Second case, less volatile trend over 20 time points. Prices as such: 1,2,3,4,5,6,7,8,9,10,9,8,7,6,5,6,7,8,9,10.
Blind DCA: Average buy price = 6.5, total returns = 53.85%
DCA up: Average buy price = 6.25, total returns = 60%
DCA up has the edge.
So it seems like for less volatile trends (or more regular DCA), DCA up > DCA blindly. For more volatile trends, DCA blindly > DCA up. And bear in mind in terms of commissions paid, DCA up is cheaper than DCA blindly because there are less trades involved for DCA up (DCA up commissions are about 30% cheaper than DCA blindly). Although the differences overall are too minute to care.
Conclusion
In a perfectly smooth market trend (that contains at least 1 downtrend), DCA up always win. DCA blindly will start to win when a certain market volatility is reached, and increases its lead as the market's volatility increases even more. So yes that explains why regular DCA is useful during volatile periods. And regular DCA is also the better option for most investors.
EDIT
Definitions:
DCA blindly = DCA at set regular time points religiously no matter the price.
DCA up = DCA at set regular time points when current price is higher than the previous, and hold if the current price is lower. Pump in that held cash in the next uptrend.
In both cases there are no market timing involved. Both methods are viable. Before you flame, I am just presenting facts and data.