Joe's Garage benefits from the same things that help any other story/concept album; it gets bonus points simply for being a larger work and having a certain degree of cohesion. Beyond that, it still has to stand on its own merits, and it does have some problems. It fizzles out in the second half. The story slows down and is nearly lost for a while, and the humorous elements are all but gone, leaving you with a bunch of guitar solos and bad narration. But some of those solos are incredible, and the story does have an ending of sorts, a la Catch-22. I've always gotten the sense that Frank himself got a little bored with the concept.
As for the instrumental side versus the "funny" side, I can't agree. Humor is subjective, and surely there will be some that doesn't work for you, but there's a lot of it, in several different flavors. Depending on my mood, I can usually find something that will make me laugh. My first exposure to Frank and The Mothers was the mid-70's band, but in college, it was the Flo and Eddie band that my roommate and I spent many, many hours listening to. You can't do that on stage anymore.