Without wishing to detract from all the factual information given by others, my view of this is a tad cynical - particularly with BA. When it comes down to it, their preferred customers (the big-ticket, silver/gold club members) will be allowed to bring on board what they please, just as now.
Who hasn't had to struggle to find overhead space anywhere near their seat because of this, or watch others bring cabin luggage on board that beggars the rules when one has been denied modest items?