There is an inverse question: If you have a cash windfall you want to invest, all-at-once or split it up?
I have seen a similar analysis (but can’t find it right now). Even if you invest at the all time highs, so the market drops right after you buy, you still win with the all-at-once strategy.
The general lesson: Get your money into the market as soon as possible. Maybe more memorable: Time in the market beats timing the market.