The partial index is highly leveraged. If every tuple in the table is
updated once, that amounts to every tuple in the index being updated
25,000 times.
How so? That sounds like O(n_2) behaviour.
If the table has 5 million rows while the index has 200 (active) rows at any given time, then to update every row in the table to null and back again would be 100% turn over of the table. But each such change would lead to an addition and then a deletion from the index. So 100% turnover of the table would be a 5 million / 200 = 25,000 fold turn of the index.
There is some code that allows a btree index entry to get killed (and so the slot to be reused) without any vacuum, if a scan follows that entry and finds the corresponding tuple in the table no longer visible to anyone. I have not examined this code, and don't know whether it is doing its job but just isn't enough to prevent the bloat, or if for some reason it is not applicable to your situation.
Cheers,
Jeff