The child doesn't, though, and, if you'll excuse my frankness, I think the abortion affects his/her future the most out of all the parties involved.
We could say that before conception, everyone agrees there is no child, and at birth, everyone agrees there is a child, so there is maybe a "spectrum" between "idea of a child" and "an actual he/she".
Your use of the wording "much more" sort of supports this "probability distribution function" idea of what a child is, and it seems like a helpful philosophical framing of this difficult and important question.
What I would say, though, is that if society is going to pick a point along that spectrum to base policy decisions on, then there is an imbalance between the risks of placing that point too early versus too late.
Too early means that some women's decisions will be unreasonably restricted, whereas too late means that some human being's lives will be unreasonably terminated.
The philosophically humble thing to do under such uncertainty would therefore be to err on the side of an earlier point, and in fact the earliest point possible, lest future generations look back on us like the slave owners or eugenicists of previous centuries.
Lack of informed consent was never central to eugenics
Additionally, you will have to pay the full price for any treatment that's outside their recommendations, this often turns out higher in absolute prices than in any US hospital - even though the people are much poorer.
Then once an unhealthy child is born they often don't get the full benefits of socialized healthcare as they should according to the constitutions, the administration will say "the system works in a different way and you went outside it, so you need to take care of it yourself" and the parents are forced to pay for treatments and medical equipment by themselves because what "the system recommends" is not nearly enough (we are talking about US$ millions of additional out-of-pocket expenses in some real world cases that I follow locally). That could be interpreted as a form of tax too, especially since you are forced to pay mandatory health insurance in most of these countries.
Historically, many cases of "eugenics" involved a lack of informed consent, even blatant coercion. That screening is entirely voluntary–you have the right to say "no", and I know couples who have (due to moral objections grounded in their religious beliefs). That's a very big difference.