A sideways thought occurs to me in relation to this thread...
Could the relatively short lifespan of modular homes be a step in the right direction from this perspective?
The person who received the Welfare payments is considered to be the head of the household. The mother will automatically get the Children's Allowance and so will automatically get the OPFP, even if the father maintains a household and has the children half the time. Jut as the mother gets a double tax free allowance but the father only gets a single persons allowance. The only way that changes is if the father goes to court and that's an expensive process where there is a perceived bias in favour of the mother. In short unless the mother is endangering the children the father won't get a look in.
Basically where a couple breaks up the mother will become the head of the household from a OPFP point of view by default. Fathers don't matter.