Operating them is not that expensive. A building's heating and cooling needs are proportional to surface area, not volume, and in a given apartment building the vast majority of walls are shared with other units instead of outside. So a taller building is more and more efficient with regards to climate control, unless it doesn't contain a whole lot of volume. The Burj Khalifa is obviously not ideal but at least judging by, say, Hong Kong the optimal sweet spot for a building is 30-40 stories, where you're not running into massive extremes of either cost or carbon emission.
The reason the suburbs perform so poorly is, among other things, transport very quickly becomes the largest contributor to emissions. Hong Kong is so dense that not only is the "fifteen minute city" more than a reality for non-work trips, but most people are within a 15 minute walk or bus ride of massive shopping malls with department stores.
That being said, the end picture looks fuzzy after some more searching, mostly because it's hard to isolate variables about cities (their wealth, their climate, etc.) and also because the definition of what a "city" is varies globally. Other than "very car oriented suburbs with large lots and home sizes are big carbon emitters per capita."