They are too big to fail and that’s why the government wants a single family to control it?

It has been working well so far. There's the old saying "don't fix it if it ain't broken." I think there's plenty of arguments to make that it is broken, but there are plenty to say it isn't. There are different views on this held by different people and different countries. Some would say break it up so it isn't too big to fail. Others say it is the size that allows it to do so well. Unfortunately the nature of the conversation is extremely complex and often these discussions turn reductionist.

TBTF is the public justification they give, but the actual reason is probably that the chaebol and government have always been very intertwined, and not always in the direction of the government exerting influence on the chaebol.

I don't know why you're being downvoted, it's a fair question.

I assume that the government doesn't necessarily care to have a single family control it. But they'd perhaps rather not push a legal campaign against that controlling family, and risk causing harm to (or retribution from) Samsung in the process.