I'm also not sure if I follow the out-of-band economic logic.
Let's imagine blocks fit exactly 10 transactions and they're all equal size. Alice needs to get their closing transaction in on time and has two options:
1. Use CPFP by paying a fee rate based on what the mempool shows, such that the combined child and parent make it into slot 9 and 10.
2. Pay the miner out of band to get the parent in slot 10, without a child transaction.
A miner would only do this if they can earn more than the fees in slot 11.
So it depends on the slope in fees. In a high fee environment I would expect this slope to be fairly low at the 4 VMB edge. But haven't run the numbers.

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