Highly automated systems + a wide variety of passenger variability = failure.
For example - and not BA or T5 - paid extra for the legroom of an emergency row exit seat (Virgin) - stand in queue for automated check in........and the machine rejects me and tells me to visit customer service, where I find that they need to check I'm not totally incapacitated if I'm sitting in that seat.
...Or the time I checked in and in front of me was a family of four (incl. two babies) returning home from a bicycle tour, complete with bikes, bike trailers, luggage, baby gear et al. Took the poor girl half an hour.
...or the time at CDG where there was a 100m queue of undocumented Africans trying to get on a flight to Britain.
Minor problems really, but now repeat that experience in Hungarian, Swahili, Mandarin, etc.
There is no substitute for plenty of experienced and helpful staff, but narcissistic management (being unable to empathise with anything or anyone) don't understand much of the human experience at all, and what they do see, they don't like. So they treat their staff as a cost of doing business.
To put it another way, from the ruthless "de - staffing" that appears to be apparent in T5, it's pretty obvious that BA management, from the Board down, see their staff as a liability, NOT an asset of the business.