Just to develop this ever so slightly.

1) In the good old days (up to the early 1990s for BA) there were 2 sorts of printed tickets. The tickets used for most of the period after WW2 were booklets, with film coated paper for each sector, giving carbon copies to the lower sheet which was the receipt. IATA set the global standard for this. This served as "money" for the airline, the gate agent absolutely had to retrieve each coupon or the airline was not paid for that passenger. These coupons could be readily endorsed to another airline if the fare rules allowed (and they normally did). Because they were so flimsy, they were put into card sleeve at check-in, where the card served as the boarding pass, and the gate agent could retrieve the coupon on boarding from the customer and hand back the boarding pass.

2) Then in the mid 1980s there came the combined ticket and boarding pass - which AA still issues with gay abandon to this day. So if you get your ticket printed out in an Admirals Club you will typically get a print of your now electronic ticket on fairly robust cardboard but in an ARC old school layout similar to 1), with the final slip being similar to the receipt page of the original paper tickets. This feeds off e-tickets, but the clever thing about this was that it also worked if the ticket was a paper ticket - instead of being a print out of that virtual ticket, it could also be the real ticket unconnected to the electronic ticket. BA started using these around 1985, but the paper aspect, for BA at least, didn't go beyond about 2005.

3) More recently BA is totally e-ticket, so the boarding pass process is now heavily divorced from the physicality of a ticket, but this gives boarding passes in a dozen different designs - apps, thermal paper, First Wing card, faxes, home printed, they just need the QR code to be scanned.

So if we go back to say the year 1995, gate agents absolutely had to collect the coupon from 1) or BA would not get paid. They may have to collect 2), depending on whether it was e-ticket or paper, and didn't really have to worry about 3) since "it's all in the cloud" / "automagical". In order for it to be clear, 2) and 3) would say "no coupon" if it was an e-ticket, so the agents could stop looking for it. In the early days of 2) the system sometimes got it wrong in both directions, so coupons were not always getting collected so there was a crackdown on printing this and on the checks.

Consequently, long after 1) has now vanished, "no coupon" to this day gets printed out. on 2) and 3) I think it must be a bit more prominent since one or two other people have raised this issue in the last couple of years.

E-Ticket - No Coupon in Red on BP?