Secondarily, if you say won a large cash lottery, you might choose to invest that over a series of spaced investments to ensure you got some kind of blended/average price rather than facing the market-timing dilemma of “should I invest this on Monday or wait until Friday?”
The premise of “time in the market > timing the market” is that all you know is that at a point sufficiently far in the future, the value will be higher.
Which means at any given point in time, if you have the ability to invest, and your goal is to achieve long term returns with low risk, then you simply invest as soon as you can. Since the longer the investment is held, the less volatile it should be. You are not trying to maximize returns, you are trying to minimize volatility.
(I agree with your approach and do not make an effort to dollar-cost-average or otherwise smooth my investments over time. But I don’t think of a pre-defined calendar based approach as “timing the market”.)
Why at regular intervals? “Time in the market” seems to imply the earlier, the better since obviously earlier means more time.