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.