I’ve been flying KLM more than BA and at EDI at least they seem to get round the need to gate check by not issuing people in the low boarding zones with an online BP. You then have to queue for a paper one and they take your trolley bag and check it in as regular luggage before you get a BP.
One of the check in staff was explicit that it was the reason no BP was available and I’ve seen it happen several times in the last 3 months, including to people connecting onto long haul flights.
It would be extra annoying if you’re in a low zone but didn’t have a trolley bag.