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The Shulchan Arach (OC 223:1) writes:
ילדה אשתו זכר מברך הטוב והמטיב
So when you have a boy you make the brocho of הטוב והמטיב.
Yet, with the birth of a girl the Mishna Berurah tells us that we make the brocho of שהחיינו.
(The Vezos HaBrocho defines the parameters well. He also notes that Sefardim are particular not to say either brocho.)
However, why is it that the brocho is gender-dependent?
You're comparing apples to oranges and wondering why they aren't the same grain. The categories don't even match.
The Talmud uses a prayer during pregnancy for a child to be male as an example of an inappropriate prayer because the gender is already determined. It also uses the birth of a son as an example of how you could hear good news in parallel to hearing that rain fell on your field. If you don't know if something is going to turn out the way you want it or the other way, then when you hear the good news you thank God. The Talmud takes for granted that having the fetus come out having always been unfortunately female was not the news you wanted. This example was not brought by the Rif or Rambam, and multiple Rishonim note that it was not generally put into practice. It is mentioned in the Tur and Shulchan Aruch, though on the spot the Rama notes that we're not talking about a formal obligation and most aren't careful about this, so the rule is definitely not anything like "when a halakhically male child moves X tefachim down from a uterus the biological parent must recite these 8 words within Y minutes and Z chalakim".
The other half of your question is the blessing celebrating seeing a friend you haven't seen in 30 days. The Shulchan Aruch rules that this is only where you have seen them before and now see them again. Some recent authorities though have argued that seeing a close family member for the first time is no less exciting than that and also warrants a blessing. If you accept that position, which is hotly debated, you can say a blessing on seeing the child for the first time if it's indeed super exciting. If you said a different blessing on hearing the child's gender, as above, then maybe you wouldn't feel inspired to bless God again on seeing the child, or maybe you wouldn't feel as emotionally pressured to rely on the opinions that a first time sighting counts in order to vent your inner joy. Some hold not like you cited that you would still say a blessing on seeing the child. (There is a large amount of discussion among modern rabbis how to handle various permutations with twins on this point.) This entire obligation is as noted somewhat novel so this could also just be one reason to reject it.
But neither of these has anything to do with birth per se, since the child isn't more valuable to your estate ex utero than in utero (and for a few years at least probably the opposite is true) and you can see the child for the first time at any age.
You're comparing a gender-news blessing with a seeing-a-friendly-face blessing and wondering why they aren't the same birth blessing. The categories don't even match.
