An important concept here is "alienated wage labour." That is labour that is performed for someone else for a wage. A wage can be money, or goods, or food. But the wage relationship is focused on "labour" on one side and "money" on the other. By considering labour as convertible into money, the nature of the labouring human is changed and their hours or days of work are reducible to accountancy. Compare to non-commuted tithes. Here a church can demand labour directly to tend land it owns. Immediate physical discipline can be used to compel labour, but more often it is compelled by a social or cultural context. This labour is not directly convertible into a dollar value, rather it is perceived in the context of the movement of seasons, increase of corn / grain, or increase of animals. This labour "does not pay its own way" because it is labour that exists outside of the accountancy concept of payment for labour.
Children in agricultural communities have for the vast majority of history not paid their own way because instead of political economy, a traditional economy has dominated. These traditional economies are governed by customs of what people do, and tend to require collective endeavour to achieve outcomes. In this context if a 4 year old is doing what is culturally required of them, they are contributing as expected. If this is tending lambs, calves, chickens, or other children they're contributing their expected amount.
In contrast, for a very short (~250 year) period there have been labourers who have been accounted for through wages and who were alienated. Here child labour pays its way if the wages bring in more than the cost of reproducing the labour power (food, clothes, rent). Jane Humphries ''Childhood and Child Labour in the British Industrial Revolution'' makes the point that the break down of pre 1789 high male wages forced working class families to send their children into alienated wage labour to keep the household functional. However, in pre factory housework children were gradually introduced into labour as part of the family / household's production of commodities. What differs between the domestic exploitation of children by parents, and the industrial exploitation of children by factory owners is the breakdown of the traditional family culture of production and its replacement with machine structured labour. For example, Hammond & Hammond's "Skilled Labourer" talks about children being used to open and close gas doors inside coal mines, or operate pumps. These children were underground as was the entire family producing the household's collective wage. Except they were not disciplined by their family (as were the frame-knitters who made stockings and socks), but by the foremen and mine owners.
In general, because the working class still exists, child labour paid its way. Families chose to "consume" additional resources on their children when their wages didn't pay for their upkeep directly, but merely defrayed losses. When children made sufficient wages, then yes they directly and individually paid their way but even wage labour families don't generally keep individuated accounts of profits and loss on children. One could argue that in certain families child labour was sufficiently loss making that these families starved to death or died of preventable disease. However, the supply of labour is social rather than individual. We might pity these individuals, but when the cost of physically reproducing labour power falls below the wage generated by that labour power, in capitalism, the supplier of that labour power the worker eventually or immediately dies. Work camps and work-to-death camps are good examples of wages below the cost of physically reproducing workers. In both the German and Soviet models, workers were explicitly paid for output in food: the relationship was fundamentally wage labour. This may be a good example, because youth tends to perish in such environments. However, due to political scruples against imprisoning four year olds in the Soviet Union for anti-soviet crimes, and due to political decisions in favour of murdering millions of Europeans in Germany we don't have examples for four year olds here.
In traditional economic arrangements children are regularly required to perform labours in order to reproduce the household. However prior to alienated wage labour there is no adequate way to determine if the child itself paid for itself because individuated labour measured in the capacity to purchase food didn't exist. Projecting a concept of a virtual wage onto medieval societies or antiquity is historically perverse anachronism. It is taking ideas and standards of one time and applying them to an other.