It is not pay per view and it shouldn't be. The child deserves to have both parents take responsibility regardless of how fair or unfair the relationship between them is.
Tax credits and child benefit are there to keep the child above the level of poverty. They are the bare minimum. Maintenance is paid on top precisely because so many NRPs weren't paying maintenance reliably and therefore the government had to stop counting it when awarding benefits.
Believe me, I spend far more on my DC than I get in tax credits or child benefit, yet they only have presents at Christmas and birthdays and we can never afford a holiday. Little things like shoes, calpol, clothes, haircuts, fuel, washing powder and extra electricity - all add up. Not to mention the cost of childcare. Maintenance would mean they could afford to have swimming lessons or I could afford to take them out once every few months. Would you begrudge them that? Any man who thinks maintenance should not be paid as soon as the mother is out of poverty is indeed bitter and not a good parent IMO.
It's fairly unusual for the mother to stay in the house unless it's rented (in which case it's not yours anyway). Apart from high earners it is not possible to sustain two housing costs and the courts will not order a NRP to pay a mortgage on the property that will leave him unable to put a roof over his own head. Likewise, a mother with dependent children, unless she is a high earner herself, will be unable to afford the mortgage by herself. In most cases, it will be sold and the asset split according to the law.
Whether or not another man moves in after the NRP has left is totally irrelevant. The relationship is over.
Seeing your children twice a fortnight? Fair enough, that's hard. I wouldn't do that to a XP (unless he was abusive or had substance abuse issues etc). Contact arrangements tend to reflect what was happening before the split though, so in cases where the NRP wasn't that hands on before the split it is obvious he's only going to get the 'every other weekend and one day in the week' deal.
It's irrelevant who earns what. Both parents created the child, both parents are responsible.
Does anybody ever refer to a NRP in real life as an NRP or an absent parent? I certainly don't and I don't think I've ever heard anyone else do it either. My X is simply "your dad" or "their father". And absent parent is just that - absent. No contact, no maintenance. That's not the same as a NRP at all.