We used to have a double McLaren buggy and two sons, 30 and 6 months old respectively. My wife travelled with them on her own. Try getting from a remote gate in T4 to the luggage carousel without the buggy. Not easy.
I think the rickety stairs argument is a bit weak: if there is an airbridge, there are stairs for when it breaks. If the stairs are safe for a passenger carrying junior I would suggest they are safe for a loader carrying an empty buggy. There is no reason to carry the buggy up the airbridge access stairs.
If there is no airbridge you put the buggy at the bottom of the stair.
The argument about drivers not allowing buggies on the bus is fatuous: every public transport operator in the UK is required to carry buggies. A child in a buggy is less at risk on a bus than in mums arms.
So, once again, safety is used as an excuse for not doing something sensible and anyone who questions is accused of not caring about safety.