Well, that's like saying "Only A Boy" should have been on Save For A Rainy Day. There was a J&D song in the can, and Dean certainly wanted to use the Jan & Dean name (no interest in releasing stuff under his own name).
But Dean would never have put "Only A Boy" on Rainy Day. Nor should he have -- because it didn't fit thematically.
For the same reason, "Only A Boy" should not have been included on Carnival of Sound (even with Jan's vocal) -- because it's not a good fit for the overall theme of the album. Same goes for "Tijuana."
Dean ran into trouble when he went to Columbia and got the tapes for "Louisiana Man." Jan's Screen Gems account got billed for Dean's work, and that's when the real trouble started. Screen Gems didn't bother with Dean's self-released material, but when he made the deal with Columbia, using the J&D name illegally, they quickly pulled the plug on Dean's single and album.
There's no way Jan would have used Dean's version of "Louisiana Man" on Carnival of Sound. Dean opted out of the counter-offer for a record deal with Columbia, and was then pressured to sign a legal contract with Warner Bros. -- which made Carnival a J&D album.
Dean could have sung on Carnival. But their working relationship was just shot by that time.
Sad but true.