Note two things about usage of like -
1. It is generally used to compare nouns
2. It means similar to
Now substitute like with similar to in the given sentence.
1. ...children process information through multiple sensory channels, like a multitude of rivers flowing into the ocean.
2. ...children process information through multiple sensory channels, similar to a multitude of rivers flowing into the ocean.
See how this makes perfect sense? That is why the use of like is right here.
As is used to describe the purpose or quality of someone or something. We can substitute as with in the form of and see if it makes sense.
1. ...children process information through multiple sensory channels, as a multitude of rivers flowing into the ocean.
2. ...children process information through multiple sensory channels, in the form of a multitude of rivers flowing into the ocean.
This is clearly wrong. Thus as cannot be used here because the comparison is similar to and not in the form of
scio me nihil scire