I think many still believe we are in the days of mostly healthy, reasonably functional young women giving up babies due to being unmarried.
In the US unmarried women do still give up babies for adoption - but via private adoptions, where a pregnant woman chooses prospective adopters to adopt her baby straight from birth. The cost of private adoption is much more than fertility treatment, it's in the region of £30-40,000. The women choose homes for their baby, and essentially adopters pay for doing so.
Adoption from the foster care system does exist obvs, with the same challenges as the UK (older children removed from the birth family's care, often additional trauma of abuse or neglect, drugs / alcohol during pregnant, and varying lengths of time in foster care between leaving their birth family and being adopted) - but with the added dynamic of race, with many more cross-racial adoptions.
David Miliband and his wife adopted their sons via private adoption in the US - they were present at their births and I believe they took the babies home from hospital. So very similar to surrogacy in many ways, in other ways very much not.
Babies leave their birth mother at birth to go home with their intended parents, large sums of money change hands, there may or may not be contact between the child and birth mother (although it's strongly encouraged but can't be enforced in both cases). In other ways the dynamic is of course very different
Does raise the question of 'buying babies' -
Private adoption (US), agreement made between adopters and birth mother before birth, birth mother retains the rights at birth to keep the baby, if she doesn't change her mind then the baby goes home with the adoptive parents. Baby isn't related to adoptive parents. Large sums of money change hands.
Altruistic surrogacy (UK), agreement made between intended parents and surrogate, surrogate retains the rights at birth to keep the baby, if she doesn't change her mind then the baby goes home with the intended parents. Baby is related to at least one intended parent. Expenses only.
They are still very very different, but adoption in the US can be very different to the UK. I don't know how often private adoption in the US is accused of facilitating baby buying.