True, although in my experience, some gate agents take it upon themselves to correct BA's vagueness and rephrase that, mostly in one of three ways:

Version 1: "We would now like to invite families travelling with infants"... : the most restrictive and arguably the most logical as they are the people who need to fold strollers at the plane door which becomes very awkward if there are people walking around at the same time.

Version 2: "We would now like to invite families travelling with children under the age of 5"... : the middle ground theory I guess. I suppose that the criterion becomes families where the parents are likely to have their hands full because they hold everyone's luggage plus kids' hands, etc.

Version 3: "We would now like to invite families travelling with children"... : the broadest description, sure to bring a few family quarrels between "come now dear" and "I'm NOT a child Mum!" 16 year old Lucy or Samantha or whatever her name is on the day. In that case, I'm not entirely sure what the logical criterion becomes. Not even giving them a chance to argue as couples do manage on their own, as do single travellers with a mobile phone.

I understand the OP's frustration that when version 3 is implemented either implicitly or explicitly, but more importantly, I would observe that by definition, if you allow versions 2 or 3, the original idea to make it easier for people with infants to settle down deal with stroller etc is immediately lost as it becomes virtually as difficult for them when 20 families are pushing behind as 200 passengers.