Just Here for Godzilla: A textbook example. The main human cast is largely interchangeable with the typical Hanna-Barbera cast, and fans generally hate Godzooky, but the battles between Godzilla and the other monsters can still make up for it.
The Scrappy: Godzooky. He gets a lot of hate from the Kaiju community, though in his defense, he's just a baby monster and may mature into something bigger and more likable if the series ever gets rebooted.
They Wasted a Perfectly Good Plot: As unloved as he is, Godzooky actually could have been the basis for a promising storyline. He's canonically said to be Godzilla's nephew—and unless the Big G is merely his Honorary Uncle, this would presumably mean that Godzilla also has at least one sibling. But for some reason, this idea was never explored, and Godzooky's parentage is unknown.
Well, technically, the original Godzilla did die in the original movie. Maybe Zooky is his kid.
What Do You Mean, It's for Kids?: This show aired during the 70s and, featuring monsters fighting every episode, was head-and-shoulders apart from other shows. But there's nothing gory or frightening for younger viewers, in this show at all. To understand the context of this trope, one has to look at and understand, the 1970s era of animation. The 70s were god awful in terms of quality, story structure, presentation and overall entertainment value. This was the era where TomAndJerry became friends, HannaBarbera was at the mercy of censors, regulations and parenting groups who held way too power and sway over the networks. Violence was NOT allowed. The significance of a Godzilla cartoon that existed during these dark times, and tried to be faithful to the source material, cannot be understated.