It's a lovely thought but not a practical one. Carbon is only one of many, many things that make a building fit for purpose. Buildings have an expiry date, too! Here in New Zealand, most buildings weren't constructed well in the first place and are best torn down.
25 years as a project manager, and I've seen crazy things. It's usually better and cheaper to start new than to adapt old. Imagine 50 years or more of ad-hoc wiring and plumbing!
Then there's code updates. Bringing the building to meet handicap access, fire protection, electrical, sprinkler, air, and seismic codes is a real problem and often impossible. Trying to heat or cool an old, poorly insulated building will cost more in carbon. Not to mention the presence of asbestos, lead paint, lead pipes, lead roofing in older buildings is a serious health risk.
Then there's insurance which favours new, and bank funding. Then there's increased density, where older buildings tend to be too short for densification. Driving in from the suburbs is far more carbon intensive than a new, taller city.
The list goes on and on. You can't be blinkered by carbon. If the building doesn't meet its obligations for safety and urban fabric, then it doesn't serve anyone well.