Akavall
Is the original sentence a typical "independent clause + coordinating conjunction + independent clause"?
If so, is a comma always optional in the above structure?
Yes, you have the right analysis of the structure. That sentence contains two independent clauses connected by a conjunction. I am of the very firm belief that you need a comma before the conjunction unless the sentence is very short and would not be confusing otherwise. I think it's also important that the reader pause before "but" because there is a transition in thought. "But" is a word that shows two conflicting thoughts.
Not everyone will agree with me. Many people don't think commas are necessary with independent clauses. I attribute this to some people not understanding how to use commas properly, so people just start hating the comma and not using it unless there's no way the sentence would make sense without it. The Associated Press has also tried to save space and ink by eliminating commas in their articles, which is where the omission of the serial comma came about. With these two factors came the trend to eliminate the comma as much as possible, and it became accepted by a lot of people...even those that understand how to use a comma properly. It boggles my mind!
Too many commas can make a sentence cluttered, but commas are your friends. Commas aid in comprehension when used properly. Leaving them out can seriously hurt the readibility factor. For instance, I edited an article the other day on proper yoga form. One of the sentences was: "When you do the yoga instructor will know you are ready for the next level." Without the comma after "do," that is a very inappropriate sentence! It trips up the reader. I had to go back and read it again to realize I was supposed to pause after "do." But many people don't think you need a comma after an introductory clause anymore. I disagree.