I've had a boarding pass reissued at the gate based on my passport.

Some airlines in Europe check both the boarding pass and the passport/identity card at the boarding gate, to ensure people haven't swapped boarding passes within the airport. I think I see this on flights outside the EU, but I'm not sure.

Speed.

It takes time to look up a passenger on a computer.

The plane will be delayed if they have to do that for everyone while boarding.

Hmm but what lookup does a human need to do? Identity documents have had chips for quite some years now so you just need to touch it to the reader and beep through, or for even older ones, they've had a machine-readable section since as long as I'm alive. A standardized government-issued passport is probably faster to read than a potentially dark and reflective phone screen or crinkled piece of paper, and equally fast in the case where the person presents a well-readable document. The gate doesn't even need to do any database lookup: it can locally store the list of the 200-odd names of passengers during boarding

I'm just speculating but if they can simply do a name+DOB-based lookup at a counter, it seems to me like the boarding pass thing might just be for historic reasons where people would feel weird if they are suddenly tracked based on personal details instead of a ticket