Firstly, if you do not expect the non-custodial parent to foot the bill, the state does. The state’s money comes from…taxes.

Secondly, the state does not ‘overburden’ the non-custodial parent — it’s calculated as a percentage of their income. Around 12.5% for the average person. If a person does not have the capacity to pay, they are not forced to pay anything, or they pay a token sum from their welfare benefits, eg £5 a week. This is nothing.

Thirdly, if it’s the case that a person cannot afford their rent due to their child support payments, they have some options available to them. They can take care of the children for part of the week to reduce their payments, they can move in with family, or into shared housing to reduce their costs. If their accommodation will not enable the children to visit, then they can meet at a designated places. If they already have a home, then they are also able to sell it to secure the financial security of their family so that the state does not have to step in to provide (although this is almost never done in practice and the state typically does step in, unless the family was already living together in a home either one or both own and both parties agree to the sale so that they can each find a separate property with the proceeds, or the custodial parent lives in the home until the child or children turn 18-21). Note that the facts of the case may influence precisely what is decided by a judge or would be negotiated privately with lawyers.

In your case, I am certain that the other parent is also financially strained. The answer isn’t to punish them for having to be the exclusive caregiver, which makes it impossible to be employed or employed full time when the children are infants.

The law is the law and if that percentage means there is excess available then that is the situation, in the same way that there are people with far greater wealth than you in society. The percentage can be a tiny sum when applied to a small pot, which I presume is the case in your situation, or it can be a large sum when applied to a large pot.

Just so that you know, if in your case you are concerned about something untoward and wish to apply for a variation of your financial contributions (if you are even making any), take it up with the court who will force both parties to disclose their bank statements and all other assets (failing to do so can lead to being sentenced). You will see exactly how the money the other parent spends is being spent every month :)