I’m looking at the code right now and it seems like I’ve found the reason.
This line of code causes the more button to show if the amount of results from the API is greater than or equal to the load limit (20, as you discovered).
Because private/deleted posts are excluded on the back-end, this causes the more results button to hide as, for example, only 19 results were returned, which is less than 20 (of course).
Seems like it can be fixed by changing how the back-end API accepts filters, possibly by adding an
hidden filter option here (and I have actually done on my own copy of the code here).
I’ve implemented these changes on my own fork of the flarum/core repo and have commented on the relevant (but misleadingly named) issue on Flarum: https://github.com/flarum/core/issues/2071#issuecomment-673455174
A filter isn’t the way the core devs want to go with, so another solution needs to be found.