Part of the point of the series was to use characters who weren't so overpowered as the Justice League characters. That is, unlike Martian Manhunter or Superman, we aren't asking "couldn't X hero just fix this by themselves easily".
That is, Superboy is strong and fast, but can't fly and doesn't have super-running speed. He also makes technical mistakes while fighting and can't keep his calm (both are unlike Superman). This means superstrong enemies can actually threaten him.
KF is fast, but not bullshit fast, which allows you to tell a story where he must run across the country to save a girl's life. He also is slow enough that capable opponents can still fight him.
Miss Martian can't transform into everything, couldn't phase through walls, and couldn't be truly invisible.
Granted, there's a few episodes where they pull a Worf and knock out Miss Martian and Superboy to provide more challenge for Robin and Artemis. But generally they avoid it.