Oops... forget to address the specific question Bill asked which was:
Should the stillborn or infant deaths have their own profiles, or only be mentioned on the profile of the parents?
I could hold up one statement from the help files, "Collaboration means one profile for every individual" as support for creating profiles for these children. (Whether or not a still born child is an 'individual' is a controversy that I will abstain from entirely)
On the other hand: 1) Since the only records that are likely to exist on these children are a record of stillbirth or a birth and death certificate, possibly an entry in a family bible, an obituary, and some sort of burial record, there is not much to colloborate on. 2) Creating profiles of children with the same name in one family can lead to erroneous merge proposals. 3) Many stillbirths either were not given names, or those names were not recorded (I commonly see them recorded as "NN") potentially resulting in a lot of profiles of first name Unknown. 4) The biography would possibly have very little reading value - there is only so much you can say about a child that never lived.
Considering the above I think:
If a family member wishes to create a profile for a stillborn child or a lost infant, as a memorial to share with family, then they absolutely should. Some beautiful words can help people through the grieving process.
From a purely research perspective, I would probably record stillbirths only on the profiles of the parents, and if they share a name with a later child that survived, on the profile of that child. The records (probably only a record of still birth, possibly an obituary, and a burial) are then accounted for, and at the same time the chances that someone will find the record of the stillborn child and change the dates on the profile for the 'survivor' is (hopefully) reduced.
Live born children that died as infants I am having a harder time forming an opinion about - Because there is likely more records than for a stillborn child, possibly even a photograph, I think a profile might be merited.