Why can't this be read as "These are the cries of children" as in, children in general rather than "the" children?
I thought the same thing, but des = de + les. I think your sentence would be "les cris de enfants"
I'm not so sure. Yes, des = de + les, but it is also the plural indefinite pronoun. I don't see any reason to use the singular de in this sentence. Can a French speaker weigh in here on why "the cries of children" would not be correct?
To compare with another example: beurre de cacahuètes is peanut butter, because it's not the butter from any specific peanuts, just butter made from any peanuts. So les cris d'enfants would similarly mean "the cries of children" in the sense of the cry that a child makes, without referencing any specific children.