Honestly the whole citizenship at birth you have newer made any sense to me.
"Jus soli" (right of the soil) is a pretty common doctrine, particularly in nations that consider themselves "free" countries. The idea is a "free" country cannot produce slaves and/or second class persons. A free country only produces free "equal" persons with equal rights, ie citizens.
The famous English case Somersett vs. Steuart led to the poetic saying that (paraphrasing)
"once a slave breathes the air of England he is made free", and similar. The 14th Amendment to the US Constitution (which was part of group the laws that ended slavery in the US) states (paraphrasing) that all persons born or naturalized in the US are citizens. One of the points of the law was to instantly grant unquestionable citizenship to all of the newly freed slaves.
I mean, what is stopping someone literally entering your country pregnant just so that they can give birth and turn their kid into a citizen
Well... border agents, laws, Courts, Judges, police, government... and so on... not to mention parental responsibility... The parent is still subject to deportation. So unless they are going to abandon their child in the US, they would take them back to their country of origin.
But I think that is besides your rhetorical point... Your point I believe, is that a person could enter/remain in the US as a non-citizen, without proper legal permission, give birth, while inside the US, and that baby would be a US Citizen as of right, under the jus soli provision of the US Constitution, found in the 14th Amendment. If that is your point then you are correct.
even if said kid would have absolutely no claim to it at all in any other circumstance?
What circumstance do you imagine supersedes the US Constitution? This isn't a technicality we're talking about here, its the Supreme law of the Land.
It's just a system that seems almost purpose designed for abuse.
Again, the principle that a free country does not allow second class persons to be born there is a very sound, moral principle. No rule or set of laws is perfect. The alternative is to allow people to be born in the US who don't have the rights of a US citizen. That is completely untenable and immoral for a free society.