There’s also a problem with variety in airport gate designs.

The same process doesn’t work well for gates which have a desk you have to go past followed by a closed lounge with seats where you wait leading to the jet bridge (LHR T3 old gates), gates which are defined as separate areas from the main terminal but have no seating area at all and little standing area either (MEX, CPH), gates where once you are scanned you just go on to the jet bridge (NCE), gates where the seats are nearby but not inside the gate area (JFK, many US airports) etc.

It also depends on whether the gate staff are BA employees or contract. Contract staff presumably have to board flights operated by many airlines and don’t bother to learn the specific processes for each one. And they may just be incentivized to do the easiest possible thing rather than follow any sort of process.