I'm convinced "Happiness Is A Warm Gun" was inspired by "She's Goin' Bald"!
I don't see it at all.
Me neither, to be honest.
While Lennon's inspiration to create a multi-part song that is made up of distinct genre types could have come from The Who's "A Quick One While He's Away" or novelty records like the kind Spike Jones used to do, "Happiness..." seems like a close approximation of "She's Goin' Bald" to me. The opening section to both songs refer to a female protagonist and have a rolling kind of melody accompanied by stream-of-consciousness wordplay. Both feature a hard blues section ("Mother Superior jumped the gun..."/"It's too late mama, there's nothing upside your head"), and both feature a parody of a doo wop style ("Happiness is a warm gun - bang, bang, shoot, shoot"/ "Na na na na, nana nana na - what a blow"). Each song contains yet another genre parody that differs from the other: "Happiness..." throws in a country-western blues nod ("I'm goin' down...") whereas "..."Bald" goes for a melodramatic radio serial jab ("She tried to salvage what she could and threw it in a sack!").
"She's Goin' Bald"'s release on "Smiley Smile" would have happened only a month or two before Lennon's trip to India when he began writing most of his material for the "White Album", so if Lennon was influenced at all by the Beach Boys' summer '67 release as he and McCartney reportedy were with "Pet Sounds", he might have been intrigued enough by "...Bald" to do his own multi-part oddity.