Alex, good post!
Just to add to that, who can claim Child Benefit? Basically either parent living with the child(ren). But what about the "No recourse to Public Funds" restriction on a time-limited spouse visa? Where that spouse is married to a British Citizen, or other EEA Citizen, then as regards Child Benefit that restriction can effectively be ignored, as para 6B of the Immigration Rules is in play. So no problem, for example, the Thai spouse of a British Citizen claiming the Child Benefit.