I agree. But they don't need to give up for a puppet government to be in place. They need to lose control of the military and communications infrastructure. If the government is far to the west or in exile, it's hard to see how they would maintain control.
And I also agree that a new government would need a substantial Russian military presence. It wasn't that long ago though that a substantial voting bloc supported pro-Russian parties. It's likely that Putin calculated that they'd only get problems with western Ukraine. That's likely been badly misjudged.
It'd be really interesting to get some polling data on those people. It's hard to imagine that they don't feel betrayed. After all, the russian speaking population has been subjected to the harshest and most violent portions of this conflict, albeit incidentally.
And there's no reason to believe that the Ukrainian government will give up once kyiv is taken, it's not a video game. In fact, western Ukraine is so terrifically safe I wouldn't be surprised if the majority of government operations are being run from there already.