Thinking about it a bit more and I don’t see a direct value in taking Kharkiv considering the inevitable costs of urban warfare. The only thing Russia needs to continue doing is not overextend themselves. As longs as they do that, they won’t loose the initiative. Getting caught in a grinding fight in the city might be inadvisable.
Kharkiv oblast was not among those officially annexed by Russia so it is not as politically important as capturing the whole of Donbass. There is a political and military value in creating a buffer zone for the Belgorod region, but that goal does not necessitate the capture of Kharkiv city.
But ofcourse you’re right that the calculation changes when there’s very little resistance.
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