"If Iranian government agrees to the inspections (which is a big question why it should), then there is no purpose for them to hide the program from their own public."

Sure there is. It's to make them appear to be defending themselves from a nefarious foreign plot. 'We cheated because we can' is not a good PR point even in those regimes.

"If Iranian government agrees to the inspections (which is a big question why it should)"

The truth of the matter is that the world doesn't want a nuclear arms race in the ME, nor do we want crazies which threatened to destroy another state to have nukes. That is treating Iran uniquely, but it's a unique regime with unique behaviour.

"So the countries which have significant nuclear stockpiles cannot go around and tell other countries to suck it up."

In our reality they can. That may not be ideal, but it is stable and prevents new world wars.

"Why do you defend sanctions as a tool, then?"

To get an inspection deal without sunsetting clauses and other loopholes, to pressure the regime to stop its malign foreign behaviour. I'd have also liked a change in the human rights situation, but that's apparently not a goal of this US administration.