Kids don't have to be super expensive!
This is true, but it's also true for most people they are. To make them not expensive, you have to avoid a lot of things that most people consider a normal, middle-class part of a regular lifestyle or a middle-class way of raising children. I won't dispute that there are probably smarter low-cost ways to raise kids, but we're talking about parents as they are and will continue to be, not parents as some idealistic frugality experts: people will want to pay for music lessons and for vacations to Disneyland. Especially if they were already taking equivalent vacations before they had kids.
Why should I have to pay for your kids?
Because collectively, people having children is what supports society, especially when it comes to people eventually retiring. If there are no more workers when it comes time for you to retire, society doesn't work. If there are not enough workers, society doesn't work well. The proportion of government budgets that different nations are paying out towards elder care via pensions and healthcare is huge and increasing because of changes in this ratio; the fewer workers you have, the more something's gotta give.
Can't we just use immigration?
This actually isn't a horrible idea, it's just that this is likely only a temporary solution, for one simple reason: birth rates are low or dropping nearly everywhere now. You can only take the excess youth from other countries for so long before that won't really work anymore. Eventually, it'll be shuffling deck chairs on the Titanic, especially as more and more developing or previously-developing countries improve their own economic situations.
There are also possible issues with cultural integration of immigrants, but I don't disagree that using immigration as part of the solution is a good idea at least for a while (and certainly, some countries already do this; the US has been below replacement rate for a while but has still had an increasing population).
What about robots doing all our work so we don't need workers?
In the sufficiently long term, yes that might work, we might get fully automated luxury communism (I'm certainly not against the idea). It's just that
a) We don't know how long it'll take until we actually have robots capable of doing all the basic things you need in a society like growing food, constructing buildings, practicing medicine, teaching people things, etc. and also
b) So far, humanity has done an awesome job of basically making up new jobs that require humans every time we get rid of existing jobs that require humans. The number of people we need to grow food has collapsed, the number of people we need for industrial production per unit of <thing> has steadily been decreasing for a long time, and yet somehow we keep coming up with more jobs for people to do, new ideas of what counts as a necessity (your great great grandparents probably didn't consider individual therapy to be one).
Well, you can make the middle-class lifestyle affordable.
It's not Disney vacations that make people give-up on childbirth. It's housing and schooling.
That's why huge subsidies to reach financial parity are probably necessary.