Posting frequency is not a ranking factor, so the cadence itself does nothing for your rankings. Google does not reward you for publishing three times a week, or four, or daily; it rewards quality and coverage, the value and completeness of what you publish, not the rhythm on which it appears. There is no schedule that pleases the algorithm, and hitting a publishing quota for its own sake adds nothing search engines can see or credit. The rule to “post X times a week to stay favored” is chasing a lever that is not connected to anything.
Where the myth comes from is a real correlation read backward. Sites that publish consistently often do rank better, and it looks like the cadence caused it, but the cadence is a side effect, not the cause. Consistency helps only indirectly, through what it produces. Publishing regularly means more quality content over time, which means more topics covered, more queries you can answer, and simply more pages with a chance to rank. The benefit is the accumulating body of good content, not the calendar that happened to produce it.
There is a freshness angle, but it is narrower than the cadence myth implies. Regular publishing can keep a site producing current material and surfacing for topics where recency matters, which helps in those specific cases. That is still about the content being timely and useful, not about the frequency being a ranking input on its own. A site that posts rarely but covers its topic thoroughly and well will beat a site that posts constantly but shallowly, because coverage and quality are what get measured, and volume without value just dilutes.
So drop the posting quota and aim at quality and coverage instead. Publish when you have something genuinely worth publishing, and let consistency serve you the real way, by steadily expanding how much good content you have and how completely you cover your topic. The goal is more pages that deserve to rank, more queries answered well, and current material where it matters, not a number of posts per week offered up to an algorithm that never asked for one.