TEXT GRAMMAR

The men pulled on the ropes to take up the slack (=to tighten them)  cf. cambridge dictionary.
The above sentence was taken from cambridge dictionary.
In this sentence, if I say ´´The men pulled on the ropes to take the slack.`` would it still give the same meaning?
or if I say ´´ The men pulled on the ropes to take up the slack.`` and another version is ´´ The men pulled the ropes to take up the slack.`` would they all give the same meaining? Why do native speakers use phrasal verbs?

I'm very impresssed with your intellectual curiosity and your perseverence!

I'll try to answer your question as best I can.

In your example of men pulling on the rope, both "to pull the rope" and to
"pull on the rope" really mean the same thing. Perhaps to "pull on" in
this instance makes it seem like more effort. This happens many times in
English -- as well as other languages -- that two different choices mean
the same thing. For example, "I live in Vienna" and "I'm living in Vienna"
really mean the same thing. Grammar books point out that the second one is
generally used when the speaker/writer thinks of it as more temporary than
the first one. But, again, the meaning is the same (the speaker/writer's
address is now in Vienna).

In the example of "to pull on" clothes, "pull on" is a phrasal verb (also
known as a two-word verb). These verbs cannot be separated to determine
the meaning (for example, it doesn't mean "pull" plus "on". Many times,
the phrasal verb seems ridiculous if you think of it as two different
words. For example, "I'm going to look up that word in a dictionary." "To
look up" is a phrasal verb meaning "I'm going to find that word by looking
through a dictionary." There is no "up" involved. You can also use the
term NOT as a phrasal verb: "Look up at the stars! Aren't they beautiful!"
Then it would mean -- literally "look" plus "up".

It's really hard to say WHY native speakers use phrasal verbs. They are
part of the language, so I guess we don't really think about it! If I
remember my History of the English Language correctly, I believe phrasal
verbs found their way into English through the influence of Germanic. The
one-word equivalents (generally considered to be more formal) are from the
influence of Latin and Greek. For example, "The police are going to look
into the matter" is the same as "The police are going to investigage the
matter." But "look into" is a phrasal verb that is less formal than the
verb "to investigate."

I hope this helps you. If it doesn't, or if you have other questions about
it, please write to me again. And I also want to say that, although I
admire your wish for "perfection", please remember that nobody really has
a "perfect" grasp of a language (not even native speakers, and not even
English teachers like me!). I'm a native speaker who has always been
interested in my language and has studied it at both university and
post-graduate level, and yet there are still things I don't understand or
keep learning about.

I would like to recommend specific books or sources for you, but it's a
bit difficult to choose. There are many websites that deal with these
questions and other language issues. Do you know about any of them? If you
like, perhaps we could meet some time at the university to talk about
these sources, or you could talk to the English teacher(s) you will have
this semester.

I wish you the best of luck in your studies, and hope that I've helped you
in some way.