How do you take Kiev without majorly damaging it?
Easy. Surround the city, cut off power and supplies and wait for a surrender from the garrison. If you wanted to be compassionate, you could open a corridor for civilians to escape & humanitarian supplies to enter. They might not use civilians as human shields as they don't consider them Russian like they did in Mariupol, but with Nazis you never know. That'll take longer but it'll have the same effect.
Either way the defenders will be forced either to starve to death or attempt a breakout (and die). There won't be a relief force coming to save them. Assaulting the city will also speed things up but will result in more friendly casualties and destroy the city.
It's the way cities were captured since human civilisation started and works just as well today.
I think there's still a couple thousand still operating in mariupol
Doubtful of that ratio, if it was true Mariupol would be in good hands already. Urban warfare is the only viable strategy for Ukraine, and considering the fact that Azov and the rest are still deeply entrenched within vast swathes of the city, its an indication that urban assaults will continue to be an arduous task.
So far, the capture of Mariupol has been the fastest I've seen a city that size being captured with urban warfare in modern military history. The speed the city is taken doesn't mean much when it comes to K/D. All it means is that defenders are retreating rather than standing and fighting. The capture of Fallujah took 1 month and the Americans had a 100+:1 K/D ratio.
What's more important is the manner the enemy is killed. Most of the Ukrainians seem to have died from traumatic injuries rather than gunfire. I.e. from was a mortar fire and buildings they were hiding in collapsed. Not as many deaths from close quarter battles. We're only getting a small data sample, what's posted by Russians on telegram, so it could be totally wrong.