Many people assume a lot of things that when investigated turn out to be false.
Often assertions don't match their backing: for example you said " The problem with this logic is that the younger the child, the more sleep they need."
However that's not what your first study says. It gives broad ranges, so it concedes that younger children can need less sleep than older children, it's not tied in a simple way to age.
You perhaps meant "on average", which is quite reasonable, and having the source you based you statement on can lead one to assume you were being brief rather than errant.
FWIW those sources look like you quickly googled it; and so weren't really relying on any particular sources.
TL;DR your source supports my observation and contradicts your claim as written.