What do you think is the issue with the adoption system? When you say "modern version", are you speaking of the foster care system?
I personally don't see a problem with IVF if the egg and sperm belong to the couple. The Bible says that God knows the baby before the baby is formed in the womb. IVF is used as an aid, in my opinion. God is still forming the child, that's why not all IVF are successful. It gets more complicated with people using egg and sperm donors, and I can see why some people have an issue with it.
I am not fully convinced about the importance of passing on the genes. Our ancestry all trace back to Adam and Eve and all humans share 99.9% same genes/DNA. In that sense, people who don't have kids still have their genes passed forward (because 99.9% of their genes/DNA is shared with someone else). God did command people to populate the Earth in the Old Testament, but in the New Testament Paul promotes the blessings of singlehood. When the disciples get disappointed that men cannot easily divorce their wives, and say it is better not to marry in that case, Jesus does not disagree. The Bible says:
11“Not everyone can accept this word,” He replied, “but only those to whom it has been given.
12For there are eunuchs who were born that way; others were made that way by men; and still others live like eunuchs for the sake of the kingdom of heaven. The one who can accept this should accept it.” There is genealogy in the Bible, but all focused towards the coming of Jesus. The genealogy is provided to show that prophecy is fulfilled. There are all sorts of people in Jesus' lineage (note Jesus' lineage is though Joseph, there is no blood relations there).