Boarding by group number is a pointless exercise on BA European and domestic flights because of time and aircraft space (single aisle) constraints and BA’s inability to manage hand luggage.
The benefit to being in group 1-3 might well just be overhead locker space but not when half the flight have BA and OneWorld Status. So many passengers now qualify for the higher groups that this just ends up being a group 1-3 queue on the jetty anyway. But I also understand that some feel a sense of importance by getting onboard the aircraft ahead of others.
On my BA Madrid flight last week, a couple (both had the DYKWIA tattoos on them essentially) approached the gate and said out loud “do all these people queueing here not know about group 1 passengers going first”. Others replied: “we are all group 1 or priority in this queue and you might need to join the back”.
On longhaul aircraft, it does make sense.