Well, just think of it this way:

Assume you've got a flight with 200 people on it who want to check something in, 3 agents, 2 hour checkin window. So each agent has to handle 66 people in 2 hours. Clearly they don't arrive nicely spaced out but even if they do that's about 2 minutes per person. Pushing it a bit, especially with multiple bags, children, faffing, overweight, etcetcetc.

Then I rock up and can't check in because my OTP-LHR-HEL-JFK-ORD-LAX-PHX-ABQ-SJC-...-BBQ itinerary across 4 carriers hasn't been reticketed properly. Agent #1 spends 45 minutes sorting the mess out (not an exaggeration from a real situation with a slightly simpler itinerary). Agents 2-3 fail to check in the growing queue and the last people miss the flight. Agent 1 hates me and BA. Agent 2-3 think "there but for the grace of deities go I". 75% of pax dislike BA. 25% of pax really hate BA. Next day there's several column inches in the Independent (Calder) or the Guardian (Tims) about how hard-done-to those people are and how BA should have a separate desk for problem nutters like me.