Can a prepositional phrase starting with "of " after the noun "use" mean who use something?

Question

I read a passage about difference between the behavior of people who feel stronger or more powerful than others and that of those who feel less strong or less powerful than others.

In this passage, an "of" prepositional phrase is used in this way:

People who felt powerful were less likely to be considerate; wealthy participants were more likely to cheat in games involving small cash rewards and to dip their hands into a jar of sweets marked for the use of visiting children.

Judging from my experiences in reading English, it seems that a prepositional phrase starting with "of " after the noun "use" means what someone uses, not who uses something, like: "The use of computers in classrooms has become common." or "a blanket ban on the use of aerosols".

I have found one example in which an "of" prepositional phrase means who uses something (from OALD 9th edition).

The bar is for the use of members only.

So I think prepositional phrases starting the word "of" after the word "use" can only mean who uses something if it is used in the form of "for the use of"

Is this thought correct? Or are there more examples other than this usage? And I'd like to know which preposition to use to mean who uses something if it exists.

I'd like to have some answer, please.

Answer 1

This use of a preposition phrase with "of" can be equivalent to a possessive (or genitive) use.

for the use of children = for children's use
this bar is for the use of members only = this bar is for members' use only

In these examples with "use", it is the children and the members who use - they are agents or actors.

That doesn't work with use of aerosols and use of computers, because aerosols and computers aren't agents, and can't use. In the case of children and members, they are actors and are not used.

With other words than "use", the same possessive structure can be used:
for the benefit of Mr. Kite = for Mr. Kite's benefit
in the name of God = in God's name

Wikipedia "English possessive"

Possessives are one of the means by which genitive constructions are formed in modern English, the other principal one being the use of the preposition of.

[emphasis added]