Can anyone give me a sensible reasoning why there should be a cut-off at security at all rather than a cut-off at the gate when the doors are closed?

Reasons I have seen are:

Passengers might delay flight - don't let passenger board at gate, no reason to stop him at security

APIS not done, no visa, seat not ready - don't let passenger board at gate, no reason to stop him at security

Checked luggage can't make it anymore - should not have been accepted and bag drop in the first place.

You will still take quite a lot of time from security to gate - I can run. Or: Gate might be close by. Thank you very much, I'll take my chances.

You wouldn't be able to make your duty free shopping anymore - true