Wow! You must have happened to get a really bum one.
We often use cast iron on ours. It works really well with cast iron.
I don't know of anything you could have done wrong to not have been able to use cast iron.
We have had none of the problems you described in many years of heavy use of ours.
What brand?
Ours is a Kenmore Elite.
Samsung. It wouldn’t work well with any black bottom pots such as Magnalite. The runaway heating was a different problem that would show up as the dials were going bad. No matter the setting it would randomly go to max heating. It didn’t matter what kind of pan I used. I like to make my own stock by simmering ckn., turkey carcass overnight but I couldn’t risk leaving the burners on even to go check the mail. Now I have a Samsung gas (propane) and love it.