> In every other scenario, the DCA is strictly worse.
Yes. And so what? It will always be the case that a lower variance approach will be better in the cases where the higher variance approach did poorly and worse otherwise.
> it's better to choose a less volatile asset allocation
These are not mutually exclusive. One can lump sum all into the lowest risk allocation and then risk on over time.
It doesn't help that right now there is not much freedom in asset allocation at all. Your choices are pretty limited to higher risk things and things with a negative real yield.
Not sure what you're using as the measure of variance, but Morningstar found DCA has higher variance in IRR: https://www.morningstar.com.au/learn/article/the-dollar-cost...
> These are not mutually exclusive. One can lump sum all into the lowest risk allocation and then risk on over time
I never said they were mutually exclusive, just that it is suboptimal.
For this to be true, you must be a successful market timer. Whatever your DCA period is, at the end of the period, you are fully invested -- a crash at that point in time would hurt you just as much as a crash would hurt a 100% equities from day 1 investor. DCA'ing is a bet that a crash will occur sometime before you are fully in. In every other scenario, the DCA is strictly worse. If you don't happen to know the timing of future crashes, it's better to put your money to work now than later, come what may.
To account for non-linearly increasing dollar utility, it's better to choose a less volatile asset allocation, not to delay your investment period.