Part of the power of sanctions are to weaken a leader's power over their people. If they lose the mandate to lead, the people may revolt and decapitate the leadership causing the issue.
It is true that that is the logic, but there are so many modern examples to show it is a flawed logic (Cuba, Iraq before the 2nd war, Venezuela, etc.). I do wish that policy makers were as open about this as they were in the early years of the Cold War, that their goal is to inflict massive pain on the population and pray for unrest. Instead, nowadays it is framed as a direct punishment on the leaders or an abstract notion like the enemy nation or their supposed ideology.
These are just falsehoods as well. America opposes Cuba and Venezuela because of socalism, not because they care about the people of those countries. The reasons for Iraq should be obvious by now.
I don't know what you think is false. I agree that the US opposed Cuba, because of socialism, and in order to counter/end socialism there, it inflicted sanctions, consciously as a means to "to decrease monetary and real wages, to bring about hunger, desperation and overthrow of government.". https://history.state.gov/historicaldocuments/frus1958-60v06...
I agree that they didn't (and still don't) meaningfully care about the people of those countries. The goal of ending socialism was not to help those people (Reagan had a lot more rhetoric about fighting socialism because he cared about the people, but I think like in the Kennedy era, this was mere rhetoric). The people are merely instrumental tools.
You don't have to be pro-socialist or anti-US to believe these things, they're quite well documented.
From my first-hand experience of being under sanctions, they do the opposite.
In 2015 Visa and MasterCard banned all transactions in Crimea. It hit hardest the people who were naturally the least loyal to Putin - the upper middle class, IT professionals, and everyone who relied on receiving international payments. I don't know anyone who has changed their opinion about Putin to worse as the result, but a lot of people, myself included, changed their attitude towards West to worse. And even if sanctions will result in the fall of the regime eventually, you can be sure they will be remembered as a hostile action.
Putin was well aware of all the possible sanctions when he gave the order, so he believes that he is prepared for the consequences.
And no, it doesn't actually work like that. If the West does come up with sanctions that significantly affect the quality of life in Russia, the Russian government will simply use it as fuel for its propaganda that the West is out to get Russia (to remind, that's the stated motivation for the invasion!).
It hasn't worked before with Putin but people still believe that if the pressure is strong enough he will change. He clearly doesn't care and no one is going to take power from him.
