The Purpose of Sanctions Against Iran is.... What?

I know, I know. Sanctions are supposedly going to convince the Iranian government to give up a nuclear weapons program that it claims it's not pursuing. Nobody believes Iran, so I guess the theory is that if economic sanctions keep piling up Iran will eventually have to deal with corrupt individuals and nations to export its oil despite the sanctions give up its nuclear weapons program. And we'll know that the sanctions worked because of their long and consistent record of failure because Iran will announce that it will have given up its nuclear weapons program and, when that time comes, for some reason its denials will suddenly seem credible. Or something like that.

I'm reminded of another nation which, after many years of economic sanctions, a militarily imposed "no fly zone", and the like, was the subject of an invasion to end its quest for "weapons of mass destruction". For a number of reasons, some quite valid, the invading nations had discounted the nation's denials of having WMD's and engaged in demagoguery about the risk posed by their non-existent weapons and non-existent delivery vehicles. After invasion we learned that the nation had abandoned its programs to develop such weapons but, you know, why worry about a wasted $trillion or two and a decade of occupation, or whether eventual blowback might make the nation or region even more dangerous - we found out for sure.

That situation was, of course, completely different. The nation's name ended with a q.

Seriously, what is Iran to conclude from the behavior of western nations? The principal lesson seems to be that if they claim to have abandoned a nuclear weapons program they won't be believed, that if they allow massive inspections of their territory they will be accused of having secret sites that they have not disclosed, and that sanctions will continue to pile up until the western world announces that the burden of maintaining the sanctions is too high and it's time to invade. (If Iran has a nuclear weapons program, it's difficult to imagine that anything short of an invasion will give any amount of certainty that it has been eliminated.) Or they can act like North Korea - develop an actual nuclear weapon. You may not get rid of the sanctions but you will significantly reduce and eventually all-but-eliminate the threat of military action. (If there's a different lesson they are likely to draw, not from the theory of sanctions but from the past behavior of western nations, please feel free to share it in the comments.)

I guess I'm just not seeing the benefit of pushing Iran to the point that it has nothing to lose by building nuclear weapons and demonstrating that it is a nuclear power. That's not the purpose of the sanctions, and I'm sure the proponents of layering misery upon misery on the Iranian people have somehow convinced themselves that "this time truly is different" and that the sanctions will "work", but at a certain point Iran will be left with nothing to lose by becoming a nuclear power - and potentially a lot to gain if it can remove a military threat from the equation. And I'm not sure how far we presently are away from that point.