Yes, I think that means testing is rarely fair, and as often as not it privileges some lifestyles over others. I don't think it matters if 'better off' parents get CB. If it were rebadged as tax relief, as it used to be, they would be paying for it via higher taxes anyway. The important thing is that all parents get it, and yes, for all children. Arguably the first child is more expensive, as items such as prams and cots can be passed down, even if clothes wear out. I never understood why my mum didn't get it for me, either. By the time my children came along, it was for all children, and (I had two) I think there was more for one than the other, but I can't remember which it was.
Restricting it to a set number of children disadvantages blended families though. If people in a new couple each have three children, for instance, it would be wrong (IMO) for the state to discourage them from becoming a household. If each parent in the new couple got tax relief for their own children it would be fairer, with arrangements being made for the ones without custody to get payments based on agreement or CMS judgements. That would, of course mean that all families with six children would have to get CB for all of them, but that would really apply to very few people, and I can't see anyone deliberately having babies to get the money. We need to encourage the birth rate anyway, with an aging society.