Quantities are the real problem here
At a wedding every wish is on the list once. With a baby it is on there five times, and that is exactly where any arrangement by message falls apart.
Without a list
"I will take bodysuits", somebody writes into the group. How many? Which size? Two others read it and hold back, although three are still missing
With a list
The wish says "2 of 5 still available". Everybody takes what they like without asking, and the count adds up afterwards
The big wish
The pram is on the list once. Whoever takes it sees at once that it is gone. That is the purchase you really do not want twice
The address
Stays hidden although delivery goes straight there. Otherwise the parcels travel to somebody else first and then across town