Let's see, in the years since 2019 I've been asked by immigration to see boarding passes 4 times that pop to mind. I am sure there were other times:

• entering China when I had had to go to HKG for an unplanned overnight trip and I did not show up as having departed PVG the day before
• exiting BRU when the immigration agent could not find the current entrance stamp in my passport and I could not find it either. To save time I showed my BP and the agent accepted that
• exiting UIO and flying via PTY and EWR to Europe, the immigration agent asked to see my itinerary and would not take my phone and asked for my "paper" itinerary or BPs
• entering MYJ with an APEC card the immigration agent said she needed to see the printed BP and made some note on it for Customs

I am on automatic mode when traveling. I know where every item is in my carry-on and I always print BPs on each trip and put them in the same place. I remove them when the trip is done. Usually don't need them but when you do, you are so glad you have them. And you don't need to rely on a phone or internet connection wherever you travel.

And most efficient. I've never delayed anyone behind me when boarding with a physical BP. However, I've been delayed at boarding by people searching their phone for an internet connection or having difficulty retrieving their BPs.