bucket approach is not a religion. No pope. No doctrine. No risk of being burned at the stake or tortured for apostasy.
To me, an AA focus and a bucket focus are just mental accounting; thinking about fungible money in ways that are useful. https://en.wikipedia.org/wiki/Mental_accounting
So we look at our portfolio both ways. AA is useful especially when thinking about volatility. Buckets are useful when thinking about liability matching. An AA that holds only long bonds may become somewhat problematic from a liability matching point of view when real estate taxes are due on Tuesday, so both views are useful for planning.
People gripe that many bucketeers don't have hard and fast rules for moving funds among buckets, but typical AA rebalancing rules produce very small changes and, from history, AAs within a fairly wide range produce the same results anyway. So, nice clean rules but basically busywork. I am quite comfortable with a flexible refill policy; sell assets when things are looking good, up to the point where the next x years of liabilities are matched with suitable asset liquidity. Done. No sleep lost.
"Cash" is another problem in many threads here. Endless threads talk about holding "cash" without specifying what that word means. I have two twenties and a five in my wallet; that is cash. Everything else is "assets" with liquidity and risk characteristics selected to suit future liability matching.
Finally, I'll predict that all AA-ers will find their inner bucketeer when they get to a point where rebalancing would require that their fixed income tranche fall below their comfort point.
So, @winpplui, there is no "the bucket strategy." It is a way of thinking about liability matching that, depending on the practitioner, comes with a varying burden of rules. DW and I usually think in terms of two buckets, near and far, or possibly three: near, far, and estate. Refills? These are basically attempts at market timing, so we'll go with our best guess.