Hi Anna,
This is a great way to look at the results. And you are certainly right in your observation that there are distance-dependent patterns. You would see a similar trend if you looked at "fraction of pairs (among all possible pairs) that are significant" for each distance bin. The reason is the underlying binomial model treating more counts as more significant observations even if the proportion is the same
(e.g., 30 out of 1000 has lower p-value than 3 out of 100). We know that and in a way, we want that because we want more sequencing depth to give us more discoveries. There are other methods that try to tackle this "p-value inflation" problem (e.g., HiC-DC) but they also have their own ups and downs.
Best,