I agree w/ OP: it's a pain. Why? B/c I only ever need 1-2 boarding passes = the one(s) for today / tomorrow. The ones after that aren't ready yet, I can't log in to get them yet anyway. What I really need is for the old ones to go away. For my purposes, I just want the old / no longer active ones to go away, they don't, so I have to either delete them every time, or else let them accumulate and delete a whole bunch at once from time to time. This is in fact a real pain. I know others may want to keep old / inactive passes for their own reasons, but defaulting to leaving them & requiring 1-by-1 manual deletion is really inefficient for my needs.
It gets worse: to delete a single pass, I first have to click once to flip it to back side to see the date, b/c date is not displayed on front. Then, there are 3 more clicks before deleting a single pass. Now, do that x 20 (I fly a lot) periodically, and yes, it's really a poor user experience.