If the design is inherently unsafe and regular use can result in injury, like the Verrückt water slide, then yes regulation and inspection is necessary. If the product is intended for children too young to understand basic safety precautions then strict design rules are important because we can’t trust companies to be ethical on their own. But if the object in question poses an obvious minor-to-moderate risk, things like trampolines or skateboards or tire swings, it can be reasonably expected that the object not break from normal use but supervision and safety precautions are the responsibility of the consumer.
There’s lots of room for argument about where the lines of acceptable risk are drawn. Personally I’m in favor of helmet and floatation-vest laws for children (and people accompanying children). I think bicycles are an acceptably risky thing for children to ride, but obviously tragic accidents do occur.
It’s hard to find data pertaining to bounce houses specifically as there is no official governing body tracking them. It gets lumped into sports or recreation and without usage stats it’s impossible to determine injury rate. They might not even be as dangerous as traditional playground structures.