This type of societal engineering isn't as easy as flipping a switch and assigning some funding to a stand-alone program. As I noted earlier, this is a wholesale reorientation of how society functions - away from class-based polices and towards natalism (I can't think of a better phrase just now.)
The money comes from reprioritizing existing spending and the spending details change over time as the effects start to show up. For instance, there is a whole lot of money that is currently being spent on the lower class. They are subsidy sucks. As the birth rate in the lower class diminishes this frees up money that would have been spent at a rate of $25,000 per capita, for instance, to now be spent at, say, $30,000 per capita on the existing members of the social class and also have some redirected to creating the upper class incentives. Fast forward 10 years and the positive feedback cycle strengthens even more.
As the human capital level of the lower class increases, they become less of subsidy sucks and some even transition into net tax contributors to society. This frees up more existing funding to be redirected towards those who are still characterized with having low human capital levels.
It's an iterative process.
True, but your framing comes across as making perfect the enemy of the good. Secondly, don't discount the influence of human capital levels on income and investment returns. The single child that arises from poverty isn't wholly dependent on a modest inheritance. They've benefited from the sole focus of their parent's attention and resources. This gives them many of the attributes that the Left believes that upper class parents confer on their children via resources and attention. Meanwhile, the upper class children are being exposed to fewer of these resources and so their human capital levels would decrease on the margin. Thirdly, as some in this thread have pointed out, their are attitudinal "deficiencies" or "ignorance" that hypothetically arise in the upper class heirs that wouldn't, or shouldn't, be present in the lower class up and comers. Those with ambition and a desire to prove themselves, along with an ability to do so, can do much with their human capital even if they are not as fully equipped with financial capital as their upper class peers. Many of those upper class people are going to be "softened" by their "gift" of free wealth and they won't have the fire in the belly of the lower class adults. This is acknowledging the liberal version of how this social psychology.
I don't understand the basis for this charge for I thought I explicitly conceded that a reduction in lower class birth rates would boost familial resources dedicated towards child rearing. If there are nutrition problems in the lower class because the lower class household has to divide resources amongst 4 children, then when there is only 1 child on the receiving end of those resources they will stretch much further. Do you disagree? This same dynamic applies to all of your stated concerns.
Recall that I noted that there has to be buy-in from both sides of the ideological spectrum. I'm not advocating the taking away of opportunities of the rich children. I'm talking about creating incentives for the rich parents to have more children. If there is any blame to be apportioned then it falls on the rich parents who have too many children, just like the same blame would fall on poor parents who have too many children.