Most people care about their findings replicating. The hard part is knowing what you need to do to improve your chances.

More like "make sure your test power is what you think it is". There will still be results that fail to replicate by virtue of the rejection of the null hypothesis by chance, but that should only happen 1 in 20 times at an alpha of 0.05. With all the bad practices that alter test power, such as p-hacking and the file drawer effect, that 1 in 20 blows up to 1 in 2.

In principle the robustness approach (redoing the analysis with some different parameters) tries to show good faith. This matters because observational studies have no meaningful replication, no second collection of data. In practice it just means practitioners gravitate towards methods more likely to show false positives.

Like, this discontinuity at zero approach seems geared to show large effects from noise. When the linear regression across the dataset is a flat line, splitting at the discontinuity pretty much mathematically requires _any_ slope have an opposite slope on the other side.

As if that was a thing you could just do? "Oh, forgot to make sure my findings replicated. I'll be sure to check that box next time, easy enough!"