This question asks about (teaching) the distinction between complex and compound sentences.
I have managed to read really quite widely in linguistics for more than fifty years without ever as far as I can recall encountering this distinction. To me it appears completely pointless and nitpicking.
Would somebody please enlighten me why it might be of any interest or value to make the distinction, never mind teach it?
I know a grammarian who maintains that it is senseless to analyse English as it is commonly spoken purely from a syntactic standpoint (while totally supporting syntactical analysis as an indispensable tool). Note however the confusion that can result from a semanto-syntactic approach:
.3. I come bearing soup, for Kate is sick.
.4. I come bearing soup, because Kate is sick.
In my book, sentence . . . 3 [is] compound, . . . conjunctive adverbs, and here FANBOYS, are both ways of linking independent clauses, and, therefore, we call them compound sentences.
Your last sentence uses the subordinating conjunction "because." With the use of "because," the second clause becomes a dependent one. It can't stand alone: "Because Kate is sick" is an incomplete thought. That's why this is a complex sentence.
Sentences (3) and (4) look suspiciously similar to me both syntactically and semantically.
............
The syntax/semantics overlap/divide can be illustrated in a few sentences.
John is tall and the car needs diesel.
(grammatical; compound; unacceptable in all but the most contrived contexts as joining two totally unrelated ideas)
John is tall and Sally is even taller.
(grammatical; compound; acceptable in that the coordinator connects two related ideas) (note however that 'Sally is even taller,' though an acceptable sentence, cannot be said to be 'semantically independent' as it needs prior context to make sense).
I come bearing soup, for Kate is sick.
I come bearing soup, because Kate is sick.
(grammatical if archaic; traditionally classified differently. 'Kate is sick' is certainly a main clause, in each case; the connecting word ('for' or 'because') while normally deducible and omissible [I come bearing soup – Kate is sick.] is, strictly, required to show the relationship (reason) between the first and second clauses. This embodies the idea of 'dependence' for 'for/because Kate is sick' if not being the usual usage.
Readers will often perceive texts that consist of mostly simple or compound sentences as uninteresting or written by immature writers. This is even more the case when the compound sentences consist of several independent clauses strung together with and's, so's and but's (so-called rambling sentences).
As OWL at Purdue states:
Adding sentence variety to prose can give it life and rhythm. Too many sentences with the same structure and length can grow monotonous for readers. Varying sentence style and structure can also reduce repetition and add emphasis.
Young writers need to be taught to recognize compound sentences and practise ways of converting them to complex or compound-complex sentences when appropriate. Understanding the composition of the four correct sentence types is helpful in identifying and avoiding problematic sentences such as run-ons, comma splices, and fragments.
I always understood it to be intended to help us focus on the difference between a dependent and independent clause. This distinction helps us recognize and form a complete, stand alone expression and to differentiate it from a phrase or fragment that cannot (at least in the context of the sentence in question).
Understanding what is needed to make a complete, independent clause would then allow us to form clear sentences. Once we understand that, we can build more complex ones. And after that, we may learn how to slice through the rules with abandon for literary effect, but using a saber that we have honed through knowledge, not forged by accident.
