The class system described provides clues
There appears to be a significant break between the Modest and Comfortable lifestyles (that same jump between Modest and Comfortable forms the basis to my answer to the question "Where does one leave a mount in a city? How much does it cost?)."
As a DM, I would require those of Modest lifestyle and lower to support each additional family member, while assuming that anyone living at a Comfortable lifestyle was already supporting their family as part of the living expenses they are paying.
The examples given of occupations in the Lifestyle Expenses section of the PHB permit a DM to make some assumptions about this pseudo-class system in a quasi-medieval world.
PHB Lifestyles
The Wretched are by definition loners, without even a fixed abode. This lifestyle cannot even sustain a family. When there is not enough for even one to survive, any additional burdens are untenable.
Squalid conditions are the lowest at which families can remain intact, for those who live in a "mud-floored hut" or a "vermin-infested boarding house". Here, each additional member is an expense. When your environment is "rife with disease, hunger, and misfortune", each additional family member is one more mouth to feed and one more burden to support.
Poor individuals cannot by themselves support a family - unskilled laborers and peddlers might form family households, but everyone in the family would be required to work in order to maintain their "simple food and lodgings" and "threadbare clothing".
Even at a Modest lifestyle, each additional family member represents a cost. "Soldiers with families" and "laborers" will have at least all of the adults of their households working, at least part of the time.
With the jump to a Comfortable lifestyle, however, it becomes possible for just one person to support an entire household. A "merchant, skilled tradesperson, or military officer" would not have their spouse, and certainly not their children, employed outside the home. Part of what makes the lifestyle 'comfortable' is that the person with income makes enough so that the other adults can concentrate their labor on making the home a better environment for its residents - cleaner, safer, with more amenities and more elaborate meals. The children concentrate on the education necessary for them to attain this class themselves when they become independent adults - laboring unpaid as apprentices. When you own a "small cottage in a middle-class neighborhood" you do not immediately worry about the additional expenses of one more child.
Working Class vs. Middle Class
The term 'middle class' is a pretty modern concept, but it can be a useful entry point to thinking about the class system implied by the Lifestyle Expenses section of the PHB. Over the span of centuries and continents, the boundary between "Working Class" and "Middle Class" is pretty fuzzy, but a few touchstones are illustrative - who has to work and whether or not they own houses and land. In Working Class households, everyone works - in the countryside, everyone in the family is contributing to the family farm. In the city, even if the head of the household has a job as a laborer or tradesperson, the other adults in the household are also working - as domestic servants in wealthier households, as nannies and wetnurses, taking in laundry or mending, etc. The children are working as well - and the poorer the family, the younger the children will be when they begin productive labor. In contrast, in Middle Class families the income of the head of household is sufficient for the rest of the family to survive without taking on additional paid labor. Not that there is not plenty of work to do in the household - just that it is unpaid labor for their own family unit. Upper Middle Class families will also hire surplus labor from Working Class families to use as domestic servants.
Oftentimes the distinction between Working Class and Middle Class will be whether they are, in the countryside, primarily tenants on someone else's land or control enough of their own cropland to support themselves. In the city, do they rent or own their own apartment or house?
To the OP's point then, at the lower categories of Lifestyle Expenses, each additional family member will be an additional expense; more mouths to feed, a larger (and more expensive) apartment to rent. Granted, each additional family member except the very youngest will also be a source of income that partially offsets their expenses - but if their income actually exceeded their expenses then either they would become their own household or the whole family would have the next higher lifestyle, so on average each additional family member is a net expense for the household.
At the higher categories of Lifestyle Expenses, however, what you are paying for is the ability to support a household without anyone else in that household having to work for pay. You are paying enough to support a group of people already, and thus within a typical family range there will not be a significant increases in expenses per additional household member. If you can afford meat at every meal you are not worried about the number of people at the table. If you can afford to own your own home, another child does not increase the cost of the property to you (maintenance and taxes).
