How is Rim Tim Tagi Dim a joke? It's about the real anxiety of becoming an independent adult and leaving home even if you love it there. Everyone knows you miss your pets the most.
Mentioning a cow and even showing cows in the music video - combined with nonsensical lyrics in the chorus -, I think it ticks a lot of boxes. It's not important if you think it's funny or not yourself - it's the intention that matters here.