More than simply a cute cartoon, I interpret "I Love to Singa" as a slight allusion to the generation gap that seemed to be taking hold in the '30s (which was itself nothing compared to what happened in the '60s). What I mean is, Depression-era teenagers and young adults would go to nightclubs and hear music by African-Americans, which the older generation didn't like. In this case, Father is the stuffy older generation, and he forbids jazz in his household. Think of him as a precursor to Archie Bunker.
So that's my interpretation. But even ignoring that, the cartoon is still quite clever (as were all the cartoons released through Warner Bros. back then). I have to admit that when I was younger, I didn't get the spoofs: Owl Jolson and Jack Bunny.