Assume the Kaiju is 200 feet tall and weighs 4,000 tonnes. The building is 180 feet tall and pretty much your average flat building. Could most buildings carry that weight on top or crawling up the side of them? Or would it simply collapse?
The answer is no, for one simple reason: contact points. Could I build a building that could support the weight of 3000-4000 medium sized cars? Yes, probably. Parking garages exist. But if I put all the cars in a huge pile in the corner of one level, they would instantly break through the floor. As soon as the kaiyu would grab the side of the building anywhere and try to pull itself up, they would take a huge chunk out of the building instead.
Most buildings are constructed to spread out the weight as much as possible, to get the most value out of as little (cheap) material as possible. Upset that balance, and you'll have a bad time.