The fact that most infants survived is not so well known because the popular TV version suggests otherwise. But you can read the NTSB report at
http://www.airdisaster.com/reports/ntsb/AAR90-06.pdf. Section 1.15.2 tells what happened to the four infants.
Perhaps some CC from UA can shed more light on this, but I think that there are several issues involved. One is the fear that babies in lap belts might be injured; another is that they could injure other passengers -- I guess that these considerations are supported by statistics somewhere. But there is a third issue: it is a hard sell for CC to tell parents to put their babies on the floor and after UA232 a parent of the baby that died confronted an FA and seemed to suggest it was her instructions that was responsible. Assigned seats would take this terrible burden off the CC.