If said investor is risk-averse, I'm not sure I would be recommending going all-in on broad market index funds either.
Generally speaking, we're here recommending approaches to young investors, whose timelines are long enough that risk shouldn't be meaningful. Based off that, the result that will produce the best return on average is not going to be DCA.
The word average is extremely misleading. What most people want is to avoid exceptionally bad outcomes, and e.g. maximize the P10 value of the portfolio in that Monte Carlo simulation.
Look no further than the Kelly Criterion to see an example of maximizing EV being worse than maximizing the median outcome.
As another example, if you have $1M and I offer you a game of chance where I flip a coin. Tails you win back 101% of your buy in. Heads I get to keep it all. The EV maximizing strategy is to put your full $1M stake. But if you follow that strategy (especially if you do so long term) is ruinous.
Generally speaking, we're here recommending approaches to young investors, whose timelines are long enough that risk shouldn't be meaningful. Based off that, the result that will produce the best return on average is not going to be DCA.