Capitalism wants not just consumption but increasing consumption. In that vein, a decreasing or stagnating population is bad for capitalism. Capitalism wants the pie to keep getting bigger.

Look at countries where population growth is negative. The economies have stagnated.

Children are essential to capitalism.

Even if granting you are correct in your identification of the problem, you offer no explanation of how an alternative system would work any differently.

I guess feudalism would increase fertility given that feudal lords need more serfs to tend their land.

I don't think there is a viable alternate system. If you have a look at past history, societies and ideas and values come and go. They rise and then they collapse. This is just the way it is.

With that said if I had to propose an idea, I would provide money to people to have children. Have the state subsidise it. Provide stay at home mums with a decent income. Fundamentally however, that will create all sorts of issues, because it doesn't change the fact that money still controls society.

Fundamentally, I think the issue is that society no longer has a set of values to propel it forward. In the past, I think values were an extension of nation (and whatever culture that entailed). Now, that value is money. Which is creating all the distortions we're seeing today.

I would argue that corporations in capitalism want and need the immigrants and babies to keep a steady customer base and consumption of their products.